Unit 4: Rational Expressions and Equations Review

Inverse Variation

100

When a quantity y changes so that the product x⋅y always equals the same nonzero constant k, this type of relationship is described by the equation y=k/x.

Inverse Variation

200

This equation is what type of variation:

xy = 15

Inverse Variation

300

This equation is what type of variation:

y/2 = x

Direct Variation

400

This equation is what type of variation:

y = x - 4

Neither direct or indirect variation

500

The time 𝑡 (in hours) that it takes a group of volunteers to organize the food donated for a Thanksgiving food drive varies inversely with the number 𝑛 of volunteers. It takes a group of 20 volunteers 4 hours to sort the food donated after each collection.  How many hours would it take if there were 25 volunteers?

3.2 hours

Graphing Rational Functions

100

f(x) = x² + 3x - 4 / x + 2.  

Find the x-intercept(s).

(-4,0), (1,0)

200

f(x)  = x² - 1 / 

6x² + 13x + 2.  

The the vertical asymptotes.

x = -2, x = -1/6

300

f(x) = 1 / x² - 9.

Find the horizontal or slant asymptotes.

y = 0

400

f(x) = x² + 3x + 2 / x +4

Find the horizontal or slant asymptotes.

y = x - 1

500

Find the end behaviors of 

f(x) = 8x - 3 / 3x + 12

As x goes to - infinity, y goes to 8/3

As x goes to + infinity, y goes to 8/3

Multiplying and Dividing Rational Expressions

100

Name the first step to simplify this rational expression:

x² - 7x + 6 / x² - 9x + 18

Factor the numerator and the denominator.

200

Find the product:

3x² - 12x / x² - 16

.   (x - 1) / 3x

x - 1 / x + 4

300

x² - 6x - 27 / 2x² + 2x 

divided by

x² - 14x + 45 / x²

x (x + 3) / 2 (x - 5)(x + 1)

400

Find the product:

x + 6 / x³ - 8

    .    (x² + 2x + 4)

x + 6 / x - 2

500

x² -8x + 15 / x² + 4x 

divided by 

x² - x - 20

x - 3 / x (x + 4)²

Adding and Subtracting Rational Expressions

100

6 / 4x³  -  

(x² - 5x + 6 )/ 4x³

5 - x / 4x²

200

Find the difference:

x + 2 / 2x - 2   -   

(-2x - 1) / x² - 4x + 3

x + 4 / 2 (x - 3)

300

x / 8 - x/4 

divided by 

x/5 - 7/10

-5x / 4 (2x - 7)

400

4/x - 3 

divided by

4/x + 5

4 - 3x / 4 + 5x

500

2 / x + 4 divided by 

3 / x - 3 + (1 / x + 4)

2 (x - 3) / 4x + 9

Solving Rational Equations

100

(x + 1) / (x - 2) = 

(x - 3) / x

x = 1

200

1 / 2x + 3 = 

x / 12x + 5

x = 5, -1/2 

300

15/x + 2/3 = 7/x

x = -12

400

(x - 1)/(x² + 3x + 2) - (2x/x + 2)

 = (x - 1)/(x + 1)

x = 1/3

500

x / 2x - 1 - (2/2x + 1) 

= x² + 20/ 4x² - 1

x = -3, 6