How to add rational expressions.

Answers

Answer 1
First, some general rules to remember:

Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:

Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.


Example 1

Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is 2(x+6)(x-6).

Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).

Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.



Step 4: Now we'll reduce the fraction to lowest terms










Example 2



Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is (x+4)(x+1)(x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.










Step 4: Now we'll reduce the fraction to lowest terms


Related Questions

Randall purchased a flat screen tv for $1089.the tax rate was 8.75%

Answers

Answer:

9528.75

Step-by-step explanation:

1089x8.75, or 1089x8 and 3/4 which is 9528.75

Find the perimeter. Simplify your answer.

Answers

Answer:

32t

Step-by-step explanation:

parallelogram. two opposite sides r equal.

2(8t+2)+2(8t-2)

16t+4+16t-4

32t

Can someone please tell me the answer to this?

Answers

Answer:

look at the picture ..........

Answer:

Step-by-step explanation:

x × [tex]x^{5}[/tex] = [tex]x^{6}[/tex]

[tex]x^{2}[/tex] × [tex]x[/tex] = [tex]x^{3}[/tex]

[tex]\frac{x^6}{x^3}[/tex]= x³

Cual es el resultado de 12/6?

Answers

Answer:

Resultado es dos (2)

Answer:

2

Step-by-step explanation:

The quotient of 2 and the sum of a number and 1

Answers

Answer:

2/(x + 1)

Step-by-step explanation:

solve pls brainliest

Answers

Answer:

Step-by-step explanation:

x= cost per gallon

10x=23

x=2.3

2.3*15= 34.5

Which of the following is a run on sentence

Answers

Answer:

B.

Step-by-step explanation:

There is no pause and the use of a connection word (and) makes the sentence seem longer. Hope this helps :) brainliest?? <3

what is 15/2 into a mixed number

Answers

7 1/2.

2 goes into 15 7 times with one left over.

The area of the pilgrims cornfield is 6,396 square feet. The width of the cornfield is 52 feed. What is the length of the cornfield? Show your work

Answers

Based on the area of the field and the width as well, the length is most likely 123 feet.

The area of the cornfield is calculated as:

= Length x Width

You have the width so you can substitute it in the equation to find the length:

6,396 = Length x 52

Solving would give:

Length = 6,396 / 52

= 123 feet

In conclusion, the length is 123 feet.

Find out more at https://brainly.com/question/20183786.

What is the ratio of apples to bananas?

Choose 1 answer:
Choose 1 answer:

(Choice A)
A
3 :4

Answers

Answer:

a

Step-by-step explanation:

it has the same a prime bundle

An Apple Watch was marked down 1/9 of the original price. If the sales price was $224 what is the original price?

Answers

Answer:

ok so that means that the new price is 8/9th of the original one so we divide 224 by 8/9=252

Hope This Helps!!!

Marked down 1/9 means it sold for 8/9 of the original price.

Divide the sale price by 8/9:

224 / 8/9 = 224 x 9/8 = (224 x 9)/8 = 2016/8 = 252

The original price was $252

13) When simplified, -2(x + 4) 3(2x + 1) is equivalent to

Answers

-6 • (x + 4) • (2x + 1)

Answer:

-6(x=4)(2x+1)

Step-by-step explanation:

Just multiply -2 x 3

Hope this helps! :)

please help me it's done in 4 mins I beg you ​

Answers

Answer:

the slope rise/run = 4/6

Which number has a prime factorization of 2x2x5x5x7x7

Answers

Answer:

4900

Step-by-step explanation:

multiply all those numbers together

2x2x5x5x7x7 = 4900

Find the area of the figure below, formed from a triangle and a parallelogram

Answers

Answer:

32 square millimeters

Step-by-step explanation:

Parallelogram area formula => B x h

Base = 6 mm

Height = 4 mm

Area = 24 mm^2

Triangle area formula B x h x 1/2

Base = 8 mm

Height = 2 mm

Area = 8 mm^2

Total area = 24 + 8 = 32 mm^2

The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters so option (C) will be correct.

What is surface area?

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

If we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

As per the given parallelogram and a triangle,

The bigger side of parallelogram = 6 + 2 = 8mm

Smaller side = 6mm

The perpendicular distance between the sides of the parallelogram = 4mm

The base of the triangle = 2mm

Height of triangle = 4 mm

Therefore, the complete area

(1/2)[8 + 6)×4 + (1/2)×2×4 = 32 mm²

Hence "The total surface area of the figure consists of a parallelogram and a triangle is 32 square millimeters".

To learn more about surface area,

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n is an integer greater than 1
Prove algebraically that 10+ n^2 - (n - 2)^2 is always an even number.
Your final line must have, 'always even' as part of the line.

Answers

Answer:

Proof below.

Step-by-step explanation:

Let f(n)=10+ n^2 - (n - 2)^2.

We want to prove f is even for integer n > or = 1.

Let's show f is even for the base case, n=1.

f(1)=10+1^2-(1-2)^2

f(1)=10+1-(-1)^2

f(1)=11-(1)

f(1)=10

f(1) is even.

Let's assume the for some integer k > or = 1 , we have f(k) is even. This means there is some integer m so that f(k)=2m.

Note: f(k)=10+ k^2 - (k - 2)^2.

We want to show f(k+1) is even.

f(k+1)=10+ (k+1)^2 - ([k+1] - 2)^2

f(k+1)=10+ (k+1)^2 - (k-1)^2

f(k+1)=10+ ((k+1)^2 - (k-1)^2)

That difference is a difference of squares. Let's try factoring it.

f(k+1)=10+ (k+1-[k-1])(k+1+[k-1])

f(k+1)=10+ (2)(2k)

Multiply:

f(k+1)=10+4k

Turns out we didn't even need to use our induction hypothesis since 10+4k is 2(5+2k) which makes f(k+1) even given the factor of 2 present.

This proves for all integers n>=1 that f(n) is even.

We could have this without induction then. Let's do that here below this line.

-------------------

10+ n^2 - (n - 2)^2

10+[n^2 - (n - 2)^2]

Factor difference of squares:

10+(n-(n-2))(n+(n-2))

Simplify:

10+(2)(2n-2)

Factor:

2[5+(2n-2)]

Because of the factor of 2, the given expression is always even for integer n.

What is the slope of the line?

Answers

The slope of this line is 2!! :)

Answer:

2

Step-by-step explanation:

Slope equals rise over run. use the slope formula

slope= (y2-y1)/(x2-x1)

find two points on the line. I used points (0,1) and points (1,3)

0=x1

1=y1

1=x2

3=y2

plug into the equation and you get

(3-1)/(1-0)=2

Help me :) !
A plant is already 41 centimeters tall, and it will grow one centimeter every month. The plant's height, h (in centimeters), after m months is given by the following function.

h(m)=41+m

What is the plant's height after 28 months?

Answers

Answer:

69

Step-by-step explanation:

Answer:

Answer

Step-by-step explanation:

H (28) = 41 + 28

H (28) = 69

Each month is +1 cm, which means 41 + 28 = 69 cm is the plant height in 28 months

There are six cookies and four friends want to share them how much will it be

Answers

Answer:

1.5 each friend

Step-by-step explanation:

6 divided by 4 = 1.5

Pleeeeeeeeeeeeeeeeeaaaaaaaaaaaaaaaaase help

Answers

Answer:IT IS 170

Step-by-step explanation:

How many sides does a polygon have if the sum of the interior angles is 360

Answers

Answer:

4

Step-by-step explanation:

we know that triangles have 180 degrees inside them and quadrilaterals are made up of two triangles, since 180 x 2 is 360 we know it's a quadrilateral.

What is free energy.

Answers

Answer:

free energy, in thermodynamics, energy-like property or state function of a system in thermodynamic equilibrium. Free energy has the dimensions of energy, and its value is determined by the state of the system and not by its history.

Erika is going to the store to buy a gallon of milk and some apples. The gallon of milk costs $3.50 and apples
cost $1.50 per pound. Use this information to complete the table, create a graph, and write an equation that
represents Erika’s total cost, C, of buying the milk and a pounds of apples.

Answers

Answer:

C = $5.00

Step-by-step explanation:

C = $5.00 because IF Erika gets 1 pound of apples they would cost $5.00

  $3.50

+ $1.50

______

$5.00

I am so srry for not being specific.

Sixteen Students Have Registered For A Summer Sports Camp. They Are To Be Divided Into Either A Swimming Or A Tennis activity, with no more than 10 students IN EITHER GROUP. in how many ways could the group in the tennis activity be chosen?

Answers

Divide 10 by 2 than separate both groups into 5 sections in each activity

There are 5 ways you could choose the group in tennis.

What is division?

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The total no of students is 16,

As there can be only a maximum of 10 students in a group,

If the student in Swimming is 10 then in Tennis it will be 6,

If the student in Swimming is 9 then in Tennis it will be 7,

If the student in Swimming is 8 then in Tennis it will be 8,

If the student in Swimming is 7 then in Tennis it  will be 9,

If the student in Swimming is 6 then in Tennis it will be 10,

Therefore, there are 5 ways you could choose the group in tennis.

To know more about division:

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Find the solution to the system of equations:

7x-8y=-23

7x-7y=-14

Answers

Answer:

Solutions: x = 7, y = 9;  or (7, 9)

Step-by-step explanation:

Given the following systems of linear equations:

7x - 8y = -23

7x - 7y = -14

Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.

    7x - 8y = -23

-   7x - 7y = -14    

             -y = -9  

Divide both sides by -1 to solve for y:

[tex]\frac{-y}{-1} = \frac{-9}{-1}[/tex]

y = 9

Substitute the value of y into either one of the given equations to solve for x:

7x - 7y = -14

7x - 7(9) = -14

7x - 63 = -14

Add 63 to both sides:

7x - 63 + 63 = -14 + 63

7x = 49

Divide both sides by 7 to solve for x:

[tex]\frac{7x}{7} = \frac{49}{7}[/tex]

x = 7

Double-check whether x = 7 and y = 9 are valid solutions to the given system:

x = 7, y = 9:

7x - 8y = -23

7(7) - 8(9) = -23

49 - 72 = -23

-23 = -23 (True statement).

7x - 7y = -14

7(7) - 7(9) = -14

49 - 63 = -14

-14 = -14 (True statement).

Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).

As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag. First the players must decide who is playing black marbles and who is playing red marbles. Then each player takes a turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. The point scheme for the game is detailed in the table below.

Point Values for Marble Game
Black Marble Points
Red Marble Points
Both black: +2 points Both red: +4 points
Different colors: –1 point Different colors: –1 point
Both red: 0 points Both black: 0 points

If Seth is challenged to a game by a classmate, which statement below is correct in all aspects in helping him make the correct choice?
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.
Both options will lose points because there are two ways to lose points and only one

Answers

Answer:

ez

Step-by-step explanation:

E(red) will be twice that of E(black), so Seth should choose to play red marbles.

Since E(red) = E(black), it is a fair game, so it doesn’t matter which color Seth chooses.

Both options will lose points because there are two ways to lose points and only one

HELP!!!!!!!!!!!!!!!!!!!!!​

Answers

Answer: A

Step-by-step explanation:

The easiest way to solve this would be to convert everything into a fraction.

9.5, 9 3/8, 9.125, 9 3/4

=

9 4/8, 9 3/8, 9 1/8, 9 6/8

So from greatest to least,

9 3/4, 9.5, 9 3/8, 9.125

So, A

Answer: The answer is F ( 9 3/4 9.5 9 3/8 9.125 )

Step-by-step explanation:

From greatest to least.

1) 9 3/4 = 9.75

2) 9.5 = 9.50 ( 9 1/2)

3) 9 3/8 = 9.37

4) 9.125 = 9.12 ( 9 1/8)

a
8) A bridge builder plans to construct a cable suspension bridge in your town. The cable being used will form
a curve modeled by the equation h(x) = 3x2 - 6x + 200, where x represents the length of cable used (in feet)
and h(x) represents the height of the cable (in feet). At what height will the cable hang closest to the bridge
deck?

Answers

Answer:

197

Step-by-step explanation:

https://www.cusd80.com/cms/lib/AZ01001175/Centricity/Domain/8294/HA2%20Chapter%202%20Review%20Key.pdf

Write the word sentence as an equation. A number divided by -8 is -13​

Answers

Answer:

104

Step-by-step explanation:

-8 * -13 = 104

104/-8=-13

Use an array and partial products to find
3 x 121.
3 x 100 = 300
3 x 20 = 60
3 x1= 3
300 +60 +3=363

Answers

Well done mate you’re correct.
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