Rational Functions

Simplify Rational Functions

100

(d^2+8d)/(2d)

(d+8)/(2)

200

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

(3x)/(x-1

300

(x^2+9x+18)/(x+6)

x+3

400

(x^2+13x+40)/(x^2-2x-35)

(x+8)/(x-7)

500

(4x^2-12x+9)/(2x^2+15x-27)

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

Multiply/Divide Rational Functions

100

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

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

200

(7x^4)/(24y^5)-:(21x)/(12y^4)

(x^3)/(6y)

300

(x^2-81)/(4x^2+27x-7)-:(x^2-5x-36)/(x^2+11x+28)

(x+9)/(4x-1)

400

(30x^3-60x^2)/(3x)-:(2x^3-16x^2+24x)

(5)/(x-6)

500

(2x^2+5x-3)/(x^2-4x)*(2x^3-8x^2)/(x^2+6x+9)

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

Graph Rational Functions

100

Find the vertical asymptote(s), horizontal asymptote(s), and hole(s) of the graph: 

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

VA: x=2

HA:y=1

holes: none

200

Describe the vertical asymptote(s), horizontal asymptote(s), and hole(s) of the graph:  f(x)=(x+3)/(x^2-9) 

VA:x=3

HA: y=0

Hole:  (-3, -1/6)

300

Describe the hole of the following graph: 

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

Hole= (-4, 4/5)

400

Find the horizontal asymptote of the graph of  y=(x^2-2x)/(-3x+9)

y=-x/3-1/3

500

Describe the vertical asymptote(s), horizontal asymptote(s), and hole(s) for the graph of  f(x)=(3x^2-5x-2)/(x^2-3x+2) 

VA: x=1

HA: y=3

Hole: (2, 7)

Add/Subtract Rational Functions

100

(3)/(12y)+(9)/(24)

(2+3y)/(8y)

200

(x)/(x+6)-(1)/(x)

{(x-3)(x+2)}/(x(x+6)

300

(x+1)/(4x^2-9)-(4)/(2x-3)

(-7x-11)/{(2x-3)(2x+3)

400

(3)/(x+4)-(1)/(x+6)

(2(x+7))/((x+6)(x+4)

500

1/x+(x-1)/5

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

Solve Rational Functions

100

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

x=4

200

(x+4)/(4)+(x-1)/(4)=(x+4)/(4x)

x=-2

x=1

300

(1)/(x)+(3x+12)/(x^2-5x)=(7x-56)/(x^2-5x)

x=21

400

(1)/(x^2-x)+(1)/(x)=(5)/(x^2-x)

x=5

500

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

x=-1