Simplify Rational Functions
{2(x-2)}/{(x-2)(x+9)}
2/(x+9)
1/3 * 5/9
5/27
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
(5)/(12)+(2)/(12)
7/12
25+45
70
(7x)/(2x^2-2x)
7/{2(x-1)}
(6x^2)/(x+2)-:(x)/(x+2)
6x
Describe the vertical asymptote(s), horizontal asymptote(s), and hole(s) of the graph: f(x)=(x+3)/(x^2-9)=(x+3)/{(x-3)(x+3)
VA:x=3
HA: y=0
Hole: x=-3
(9)/(10)-(1)/(5)
7/10
How do I find the y-intercept of a simplified rational expression?
(x-5)/(x^2-25)
1/(x+5)
(5)/(x+6) *(x+2)/(x+4)
(5x+10)/(x^2+10x+24)
Describe the x-intercept and y-intercept of the following graph: (write answer as a point)
y=(x^2+7x+12)/(x^2+3x-4)={(x+4)(x+3)}/{(x-1)(x+4)}
x-intercept:(-3,0)
y-intercept:(0,-3)
(x+1)/(x^2-9)+(x+7)/(x^2-9)
(2x+8)/(x^2-9)
What are the factors of
x2-1
(x+1)(x-1)
(x^2+9x+18)/(x+6)
x+3
{(x+2)}/{(x^2-4)}-:(x+3)/(x-2)
1/(x+3)
Find the horizontal asymptote and end behavior of the graph of y=(x^2+24x-25)/(3x^2+6x+5)
As \ \x \rightarrow \-infty \, f(x) \rightarrow ?
As \ \x \rightarrow \infty \, f(x) \rightarrow ?
H.A: y=1/3
End Behavior: 1/3
(3)/{(x-4)(x+4)}+(x+3)/(x-4)
(x^2+7x+15)/({(x-4)(x+4)}
When dividing a rational function what do we do?
Keep first fraction change sign and flip second fraction
(x^2+13x+40)/(x^2-2x-35)
(x+8)/(x-7)
(x+7)/(x+8) *(x^2+x-56)/(x^2-49)
1
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: X=2
(3)/(x+4)-(1)/(x+6)
(2x+7)/{(x+6)(x+4)}
How do we find the horizontal asymptote?
look at the degrees