TM:CA Rational Operations

Simplifying Rational Expressions

100

Simplify the expression completely: 

(x² - 2x) / (5x³)

(x - 2) / 5x²

200

Simplify the expression completely: 

(9x) / (36x² - 180x)

1 / 4(x - 5)

300

Simplify the expression completely: 

(x² - 5x - 6) / (x² - 1)

(x - 6) / (x - 1)

400

Simplify the expression completely: 

(x⁴ + 8x³) / (x² + 5x - 24)

x³ / (x - 3)

500

Simplify the expression completely: 

(x² - 5x - 6) / (x² - 1)

(x - 6) / (x - 1)

Multiplying/Dividing Rational Expressions

100

Perform the following operation and express in simplest form: 

(x + 7) / (x + 8) * (x² + x - 56) / (x² - 49)

1

200

Perform the following operation and express in simplest form: 

(x² - 1) / (x² - 6x + 5) * (3x - 15) / (6x)

(x + 1) / 2x

300

Perform the following operation and express in simplest form: 

[(x² - 11x + 30) / (x - 6)] / [(x² - 12x + 35) / (9x³)]

9x³ / (x - 7)

400

Perform the following operation and express in simplest form: 

(9x + 72) / (x² + 10x + 16) * (x² - 7x - 18) / (x - 9)

9

500

Perform the following operation and express in simplest form: 

(x² - 5x - 36) / (8x + 32) * (x - 7) / (x² - 16x + 63)

1/8

Adding/Subtracting Rational Expressions

100

Combine the following fractions and express in fully reduced form:

3 / 4x + 5 / 4x² 

(3x + 5) / 4x²

200

Combine the following fractions and express in fully reduced form:

3x / 5 - 2x / 9

17x / 45

300

Fully simplify to one fraction:

3x / (8 - x) + (7x + 1) / (x - 8)

(4x + 1) / (x - 8)

400

Fully simplify to one fraction:

(7x + 1) / (x² - 36) + (3x) / (x + 6) 

(3x² - 11x + 1) / ((x - 6)(x + 6)) 

500

Fully simplify to one fraction 

(7x + 5) - (1) / (x + 6)

(7x² + 47x + 29) / (x + 6)

Rational Equations

100

Solve for all values of x 

(x) / (x - 6) = (1) / (x - 6)

x = 1

200

Solve for all values of x:

- 5 + (3) / (x - 3) = (4x) / (x - 3)

x = 2

300

Solve for all values of x:

(x) / (x - 1) + 8 = (1) / (x - 1)

x = NO SOLUTION

400

Solve for all values of x:

x - (1) / (x - 3) = (3) / (x - 3)

x = 4, - 1

500

Solve for all values of x:

x - (x) / (x + 2) = (2) / (x + 2)

x = 1

Vocabulary

100

Shared by, coming from, or done by more than one

What is common?

200

The number below the line in a common fraction; a divisor.

What is the denominator?

300

Resolve or be resolvable into factors.

What is factoring?

400

An equation in which two ratios are set equal to each other.

What is a proportion?

500

A function that is the ratio of two polynomials

What is a rational?