# How do you simplify (2x-10)/(25-x^2) and what are the excluded values for the variables?

Aug 2, 2017

Given: $\frac{2 x - 10}{25 - {x}^{2}}$

Factor out -2:

$\frac{- 2 \left(x - 5\right)}{{x}^{2} - 25}$

Factor the denominator:

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

Please observe the canceled factors:

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

Remove the canceled factors and append the excluded value:

(-2)/(x+5); x!=-5