Algebra 2 Rational Expressions Review

simplifying rational

100

Simplify: (2a² +10a) / (3a² + 15a)

What is 2/3 

200

Simplify:

(x²+x−6) / (x² +8x+15)

What is  (x-2) / (x+5) 

300

Simplify:

((4x+20) / x² ) *  ((x²+x) / (2x+10))

What is 2(x+1) / x

400

Simplify:

(3x² - 13x - 30) / (18x² - 50)

What is (x-6) / 2(3x-5) 

500

Simplify:

(8x² - 46x + 45) / (4x² - 17x + 5)

What is (2x-9) / (x-3) 

Multiplying and Dividing

100

Simplify:

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

What is 7/2 

200

Simplify:

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

What is (2x-3) / 4x³

 

300

Simplify:

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

What is x²-9 

400

Simplify:

((3x² + 13x + 4) / (4x² - 16)) divided by ((8x + 32) / (4x + 8))

What is (3x + 1) / (8x - 16) 

500

Simplify:

((4x² + 20x) / (x³ + 4x²)) TIMES ((x² + 8x + 16) / (8x² + 36x - 20))

What is (x+4)  / (2x²-x) 

Addition and Subtraction

100

Simplify:

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

What is 5 

200

Simplify:

(x² / (x + 5)) + ((7x + 10) / (x + 5))

What is x + 2

300

Simplify:

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

What is 3 / (x + 4)

400

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

What is 1 / (x + 5)

500

Simplify:

((6y - 6) / (y² + 4y - 12)) - ((y +4) / (y² + 4y - 12))

What is 5 / (y + 6)

Equations

100

Solve:

(4 / x) + x = 5

x = 1 and 4

200

Solve.

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

x = 1/4

300

Solve.

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

x = -1

400

Solve.

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

x = -1/2 and 3

500

Solve.

3x / (x + 1) = (12 / (x² - 1)) + 2

x = -2 and 5

Mystery...

100

Find the excluded values for the expression:

(3x³-3x²-18x) / (6x³-36x²+54x)

What is x=0,3

200

Find the domain for the expression:

(x³-3x²) / (2x²-6x)

What is all real numbers such that x is not equal to 0,3

300

Factor:  3x² - 5x - 2

What is  (2x + 3) (3x + 1)

400

Find the value of the discriminant:

 9x² - 8x =-3

What is -44

500

Find the vertex of the quadratic function:

f(x)=  5x² +10x- 4

What is (-1,-9)