Question

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

Answer 1

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

Explanation:

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.