Algebra 2 Rational Expressions Review

simplifying rational

100

Simplify: (2a² +10a) / (3a² + 15a)

What is 2/3 

200

(x²+x−6) / (x² +8x+15)

What is  (x-2) / (x+5) 

300

((4x+20) / x² ) *  ((x²+x) / (2x+10))

What is 2(x+1) / x

400

(3x² - 13x - 30) / (18x² - 50)

What is (x-6) / 2(3x-5) 

500

(2x² - 7x -9) / (x² - 2x -3)

What is (2x-9) / (x-3) 

Multiplying and Dividing

100

(7x / (2x - 10)) divided by (x² - 6x) / (x² - 11x + 30)

What is 7/2 

200

(6x² + x - 15) / 4x² divided by (3x² + 5x)

What is (2x-3) / 4x³

 

300

(x² - 3x) / (x - 2) TIMES (x² + x - 6) / x

What is x²-9 

400

(3x² + 13x + 4) / (4x² - 16) Divided by (x + 4) / (4x + 8)

What is (3x + 1) / (x - 2) 

500

(4x² + 20x) / (x³ + 4x²) TIMES (x² + 8x + 16) / (x² + 9x + 20)

What is 4/x

Addition and Subtraction

100

(5x / (x + 3)) + (15 / (x + 3))

What is 5 

200

((x + 6) / (x² - x - 20)) + ((2x - 21) / (x² - x - 20))

What is 3 / (x + 4)

300

(  (4x - 7) / (x² - 25)  ) MINUS (  (3x - 2) / (x² - 25)  )

What is 1 / (x + 5)

400

(x-2) / ( x2 +5x+6) MINUS  5 / (x+3)

-4/(x+2)

500

(  a / (a² - 25) )  MINUS   (  2 / (a² - 9a + 20)  )

(x² - 6x - 10) / (x-5)(x+5)(-4)

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 / (x² - 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  (x-2) (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)