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

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Answer 1 · 2016-05-11T18:10:21

$(a-b)^2/(b-a) = b-a$ excluding $a=b$

For any number $x$ we have:

$(-x)^2 = x^2$

So:

$(a-b)^2/(b-a) = (-(a-b))^2/(b-a) = (b-a)^2/(b-a) = ((b-a)color(red)(cancel(color(black)((b-a)))))/color(red)(cancel(color(black)((b-a)))) = b-a$

excluding $a=b$

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

$(a-b)^2/(b-a)$

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

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