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

Feb 7, 2016

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

#### Explanation:

In this case the denominator is,
$\left(2 x - 3\right) \left(7 x - 3\right)$
now put $\left(2 x - 3\right) \left(7 x - 3\right) = 0$
$\implies$ either $\left(2 x - 3\right) = 0$ or $\left(7 x - 3\right) = 0$
if $\left(2 x - 3\right) = 0$
then $2 x = 3$ $\implies$ $x = \frac{3}{2}$

and if $\left(7 x - 3\right) = 0$
then $7 x = 3$ $\implies$ $x = \frac{3}{7}$

so $x = \frac{3}{2}$ and $x = \frac{3}{7}$ are the vertical asymptotes.