Question

Simplify the equation: ((a-b)(a+b)) / ((b-a)(b-a))

Answer 1

Hint: b-a = -a + b = -(a - b)

Answer 2

b-a = -(a - b)

so

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

(b-a)(b-a) = (-1)*(-1)*(a-b)(a-b)

(b-a)(b-a) = 1*(a-b)(a-b)

(b-a)(b-a) = (a-b)(a-b)

Answer 3

That means

\[\Large \frac{(a-b)(a+b)}{(b-a)(b-a)}\]

turns into

\[\Large \frac{(a-b)(a+b)}{(a-b)(a-b)}\]

Answer 4

OH! That makes so much more sense. Thank you so much.

Answer 5

I'm sure you see what to do from here. What do you get?

Answer 6

You get \[\frac{ a+b }{ a-b }\] right?

Answer 7

very good, a pair of (a-b) terms cancel out

Answer 8

Thank you!

Answer 9

you're welcome