Algebra 2 Rational Expressions Review

simplifying rational

100

Simplify:

(2a^2 +10a) / (3a^2 + 15a)

What is

2/3

 

200

(x^2+x−6) / (x2 +8x+15) 

What is 

(x-2) / (x+5) 

300

((4x+20) / x^2 ) * ((x^2+x) / (2x+10))

What is 

(2(x+1)) / x 

400

(3x^2 - 13x - 30) / (18x^2 - 50)

What is 

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

500

(8x^2 - 46x + 45) / (4x^2 - 17x + 5)

What is 

(2x-9) / (x-3) 

Multiplying and Dividing

100

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

What is 

7/2

200

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

What is

(2x-3) / (4x^3) 

 

300

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

What is x²-9 

400

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

What is 

(3x + 1) / (8x - 16) 

500

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

What is 

(x+4) / (2x^2-x) 

Addition and Subtraction

100

1/4 + x/3

What is 

(4x+3)/12

200

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

What is x + 2

300

((x + 6) / (x^2 - x - 20)) + ((2x - 21) / (x^2 - x - 20)) 

What is 

3 / (x + 4)

400

((4x - 7) / (x^2 - 25)) - ((3x - 2) / (x^2 - 25)) 

What is 

1 / (x + 5) 

500

((6y - 6) / (y^2 + 4y - 12)) - ((y +4) / (y^2 + 4y - 12)) 

What is

5 / (y + 6) 

Equations

100

(4 / x) + x = 5 

x = 1 and 4

200

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

x = 1/4

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 - 8x + 16

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

500

Factor:  25x² - 4

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