# How do you find the discontinuity of a rational function?

Aug 29, 2014

The discontinuities of a rational function can be found by setting its denominator equal to zero and solving it.

Let's look at a simple example. Let us find the discontinuities of $f \left(x\right) = \frac{x - 1}{{x}^{2} - x - 6}$.
By setting the denominator equal to zero,
${x}^{2} - x - 6 = 0$
By factoring it out,
$\left(x + 2\right) \left(x - 3\right) = 0$
So, we have $x = - 2$ and $x = 3$.
Hence, $f$ is discontinuous at $x = - 2$ and at $x = 3$.

Would this get you going?