What is/are the vertical asymptote(s) for #y=(x^2+2x)/(x^2+5x-6)#?
The vertical asymptotes are where the denominator is equal to zero, because you can't divide by that. Therefore you should use factorisation here for the denominator:
We set this equal to zero, and find
To find the vertical asymptote of any function all we need to do is find where this function is undefined.
If a function is undefined when its' denominatore equals 0 (dividing by 0) then we can find the vertical asymptote by taking the denominator and setting it equal to 0.
Now we can factor this piece of the function.
We have 2 vertical asymptotes because we have 2 numbers that make the denominator=0
The denominator is 0 if