a-b/b-a algebraic fraction

Question

I'm trying to figure out the solution to a-b divided by b-a

Answer 1

(a-b)/(b-a) = (a-b)/[-(a-b)]

 

Cancelling the a-b factors, we get -1.

Answer 2

Multiply numerator and denominator by a+b and simplify.

 

[(a - b) / (b - a)] * [(a + b) / (a + b)] = (a² - b²) / (b² - a²) = (a² - b²) / [-(a² - b²)] = -1