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Multiply/ Divide
Add/ Subtract Rationals
Simplify
Rational Equations
Vertical/ Horizontal Asymptotes
Holes
x/y intercepts
Undefined
100

x /(8 x + 48) ÷ (x^2+ 11 x + 18)/ (x^2 + 8 x + 12)

x/(8(x+9)

100

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

(x-1)/x

100

1 + (2 x)/ (x + 4 )= − 8 /(x + 4) 

No Solution

100

 Find the horizontal asymptote

f(x)= ((x−7)(x−6))/(3(x+9)(x−6))   

y=1/3

100

Which values of x are undefined

(x^2-1)/(x^2+15x+54)

x=-6 x=-9

200

Express in reduced form

(−4x−6)/(2x^3)  + ( 8x−1)/ (2x^3) 

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

200

(x^2-49)/(6x+42)

(x-7)/6

200


 x+7/(x-6)=2x 

x=-1 & x=7

200

 Find the horizontal asymptote

f(x)=(x^2-11x+24)/(2x^2-16x)

y=1/2

200

Find all x intercepts

f(x)= (3x+2)/ (x−5 ) 

(-2/3,0)

300

(x^2 -36)/ (x^2-5 x -6) ⋅ (3 x + 3 )/(9x^2)

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

300

(x^2 +7x+12 )/(x^2 −9x)

(x+4)/(x+3)

300

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

Reject x=2 

x=-1

300


Find the vertical asymptote

 f(x)=(3x^2 −30x+27 )/(x^2-13x+36) 

x=4

300

find the y intercepts

f(x)=(4x−2)/( 2x^2 −15x+7) 

y=(0,-2/7)

400

5/x-6/(7x)

29/(7x

400

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

2

400

x-(3x)/(x+7)=5/(x+7

x=1 x=5

400

find the horizontal asymptote

f(x)=(15x-6)/(x^2+4x-45)

y=0

400

Find the x intercepts

f(x)=(x−7)/(2x^2 −20x+42)

no x-intercepts

500

 (x^2 −81)/(x^2 −x−72)  ÷  (x−2)/(x+8)  

( x + 9 ) /(x−2) 

500

(24x^2-72x)/(8x)

3(x-3)

500

9 − x /(x + 3) = − 5 /(x + 3 )

x=-4

500

 f(x)=(3x^2+6x-189)/(x^2-17x+70) 

Find the vertical asymptote

x=10

500

Find the hole 

f(x)=(x^2-10x+24)/(2x^2-12x)

(6,1/6)