Question

For what values of x, if any, does `f(x) = 1/((5x+3)(x-6)` have vertical asymptotes?

Answer 1

`"vertical asymptotes at "x=-3/5" and "x=6`

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.

`"solve "(5x+3)(x-6)=0`

`x=-3/5" and "x=6" are the asymptotes"`
graph{1/((5x+3)(x-6)) [-10, 10, -5, 5]}