SOLUTION: I really need help with rational functions! Please help me with the following: I need to find the zeroes, poles and asymptotes, then sketch x(x-1)(x-5)/(x+1)(x-3)(x-4) Thank

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I really need help with rational functions! Please help me with the following: I need to find the zeroes, poles and asymptotes, then sketch x(x-1)(x-5)/(x+1)(x-3)(x-4) Thank       Log On


   

Question 341388: I really need help with rational functions! Please help me with the following:
I need to find the zeroes, poles and asymptotes, then sketch
x(x-1)(x-5)/(x+1)(x-3)(x-4)
Thank you very much!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Zeros make the numerator equal zero.
x%28x-1%29%28x-5%29=0
Three solutions:
x=0
.
.
.
x-1=0
x=1
.
.
.
x-5=0
x=5
.
.
.
Vertical asymptotes occur when the denominator equals zero.
%28x%2B1%29%28x-3%29%28x-4%29=0
Three solutions:
x%2B1=0
x=-1
.
.
.
x-3=0
x=3
.
.
.
x-4=0
x=4
.
.
.