Rational Functions Review

Multiplying and Dividing Rational Functions

100

Simplify

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

5

200

Multiply

((a^2+7a+12)/(a^2-9))*((a-3)/(a+3))

(a+4)/(a+3)

300

Divide. 

(c^2-c-12)/(c^2+4c+3)

and 

(c^2-6c+8)/(c^2+5c+4)

(c+4)/(c-2)

400

Multiply

(x^2-25)/(4x-20)*1/(x^2+6x+5)

(1)/(4(x+1))

500

Simplify

((3x+6)/(x+5))/((x+2)/(x^2-25))

3(x-5)

Adding and Subtracting Rational Functions

100

Subtract

(x+12)/(2x-5)-(3x-2)/(2x-5)

(-2x+14)/(2x-5)

200

Add

(x+4)/(x^2-x-12)+(2x)/(x-4)

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

300

Simplify

x/(x-4)-(6x)/(x-5)

(-5x^2+19x)/((x-4)(x-5))

400

Add

(1)/(12xy^2)+(3y)/(10x^2)

(5x+18y^3)/(60x^2y^2)

500

Add

(3x^2)/(16x^2-1)+(2)/(4x+1)-(x)/(4x-1)

(-x^2+7x-2)/((4x+1)(4x-1))

Solving Rational Equations

100

Solve

(1)/(x)-(x-2)/(3x)=(4)/(3x)

x = 1

200

Solve

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

x = 0

300

Solve

(56)/(x^2-2x-15)-(6)/(x+3)=(7)/(x-5)

No solution 

(x = 5 is extraneous)

400

Solve

(2x-9)/(x-7)+(x)/(2)=(5)/(x-7)

x = -4

(x = 7 is extraneous)

500

Solve

(x^2-4)/(x+3)+(x-2)/(x+3)=2

x = 4

(x = -3 is extraneous)

Analyze Graphs of Rational Functions

100

What is the Vertical Asymptote of the function: 

(2x-3)/(x-4)

x = 4

200

What is the Horizontal Asymptote of the function: 

(2x-3)/(x-4)

y = 2

300

Find the hole in the function: 

(x^2-64)/(x^2+9x+8)

(-8, 16/7)

400

Identify the x and y intercepts in the function: 

(x-4)/(3x-8)

x-intercept: (4, 0)

y-intercept: (0, 1/2)

500

Find the asymptotes of the function: 

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

VA: x=1/2

HA: none

Oblique asymptote: y= (1/2)x + 5/4