Question

For what values of x, if any, does `f(x) = 1/((2x-3)(7x-3)` have vertical asymptotes?

Answer 1

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.

Explanation:

In this case the denominator is,
`(2x - 3)(7x - 3)`
now put `(2x - 3)(7x - 3) = 0`
`=>` either `(2x - 3) = 0` or `(7x - 3) = 0`
if `(2x - 3) = 0`
then `2x = 3` `=>` `x = 3/2`

and if `(7x - 3) = 0`
then `7x = 3` `=>` `x = 3/7`

so `x = 3/2` and `x = 3/7` are the vertical asymptotes.