Question

I need Help simplifying!

Answer 1

\[\frac{ 4x-12 }{ x ^{2}-9 }\]

Answer 2

Ok, so 4x-12 = (3x + x) - (3 + 9), correct?

And x^2 - 9 = (x+3)(x-3), do you understand this?



So, now you have:

(3x+x-3-9) / [ (x+3)(x-3) ]


And this is equivalent of having:
( 3x-9 ) / (x+3)(x-3) + (x-3) / (x+3)(x-3)


Which is:

3(x-3) / (x+3)(x-3) + (x-3) / (x+3)(x-3)

= 3/ (x+3) + (x-3) / (x+3)(x-3)
= 3/ (x+3) + 1 / (x+3)
= 4/ (x+3)

Answer 3

@Diogo Okay thank you! i didn't know that you turn the numerator into (3x+x-3-9)
But it makes sense now!