# How do you simplify (a-b)^2/(b-a)?

May 11, 2016

${\left(a - b\right)}^{2} / \left(b - a\right) = b - a$ excluding $a = b$

#### Explanation:

For any number $x$ we have:

${\left(- x\right)}^{2} = {x}^{2}$

So:

${\left(a - b\right)}^{2} / \left(b - a\right) = {\left(- \left(a - b\right)\right)}^{2} / \left(b - a\right) = {\left(b - a\right)}^{2} / \left(b - a\right) = \frac{\left(b - a\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(b - a\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(b - a\right)}}}} = b - a$

excluding $a = b$

The exclusion is necessary because if $a = b$ then $b - a = 0$ resulting in a zero denominator in the expression:

${\left(a - b\right)}^{2} / \left(b - a\right)$

and the result of division by $0$ is undefined.