Algebra 2 Rational Expressions Review

simplifying rational

100

Simplify:

 (2a^2 +10a) / (3a^2 + 15a) 

2/3

200

Simplify:

 (x^2+x−6) / (x^2 +8x+15) 

(x-2) / (x+5)

300

Simplify:

 (4x+20) / x^2 * (x^2+x) / (2x+10) 

(2(x+1)) / x

400

Simplify:

 (3x^2 - 13x - 30) / (18x^2 - 50) 

(x-6) / (2(3x-5))

500

Simplify:

 (8x^2 - 46x + 45) / (4x^2 - 17x + 15) 

(2x-9) / (x-3)

Multiplying and Dividing

100

(7x) / (2x - 10) divide (x^2 - 6x) / (x^2 - 11x + 30) 

7/2

200

(6x^2 + x - 15) / (4x^2) divide (3x^2 + 5x)

(2x-3) / (4x3)

 

300

 (x^2 - 3x) / (x - 2) * (x^2 + x - 6) / x 

x^2-9

400

 (3x^2 + 13x + 4) / (4x2 - 16) divide (8x + 32) / (4x + 8) 

(3x + 1) / (8x - 16)

500

(4x^2 + 20x) / (x^3 + 4x^2) * (x^2 + 8x + 16) / (8x^2 + 36x - 20)

(x+4) / (2x^2-x)

Addition and Subtraction

100

 (5x) / (x + 3) + 15 / (x + 3) 

5

200

 (x^2) / (x + 5) + (7x + 10) / (x + 5) 

x + 2

300

n/(n^2-2n-3)-1/(n^2-5n+6)

(n^2-3n-1)/((n+1)(n-3)(n-2))

400

x/(x^2-4)+1/(x-2)

(2x+2)/((x-2)(x+2))

500

t/(x^2-25)-1/(t^2-10t+25)

(t^2-6t-5)/((t-5)(t-5)(t+5))

Equations

100

4 / x + x = 5

x = 1 and 4

200

2 / (3 x) + 1 / 6 = 4 / (3 x)

x = 4

300

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

x = -1

400

(x - 1) / x + (2x - 1) /(x + 3) = (x + 6) / (x + 3)

x = -.5 and 3

500

(3x) / (x + 1) = 12 / (x^2 - 1) + 2 

x = -2 and 5

Factoring

100

Factor:  x² + 4x - 45

What is (x + 9) (x - 5)

200

Factor: x² - 9x + 20

What is (x - 4) (x - 5)

300

Factor:  3x² - 5x - 2

What is  (2x + 3) (3x + 1)

400

Factor: 9x² - 24x + 16

What is (3x - 4)2 or (3x - 4) (3x - 4)

500

Factor:  25x² - 4

What is (5x + 2) (5x - 2)