How do you simplify and find the excluded values of (x-2)/(x^2+3x-10)?

Jun 8, 2016

$\frac{1}{x + 5}$, but $x \ne - 5 \mathmr{and} x \ne 2$

Explanation:

The denominator of the fraction can be factorised.

$\frac{x - 2}{\left(x + 5\right) \left(x - 2\right)}$

The denominator may not be zero, so we need to find which values of x would give 0 for each factor.

If $x + 5 = 0 \Rightarrow x = - 5$ and if $x - 2 = 0 \Rightarrow x = 2$

The fraction simplifies to

$\frac{\cancel{x - 2}}{\left(x + 5\right) \cancel{x - 2}} = \frac{1}{x + 5}$