How do you subtract $9/(x^2-9) - 5/ (x+3)$ ?

Question

1838 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-29T11:55:20

I have shown every step in 'over the top' detail so you can see where everything comes from.

$- (5x-24)/(x^2-9)$

When presented with questions you look for links which means you have to build up a 'toolbox' of remembered facts and techniques:

Given: $9/(x^2-9) - 5/(x+3)$ .............(1)

Consider $x^2-9$ ....................(2)

But $9 = 3^2$ .....................(3)

Substitute (3) into (2) giving:

$x^2 - 3^3$

But $(x^2-3^2)=(x-3)(x+3)$ ........(4)

Substitute (4) into (1) giving:

$9/((x-3)(x+3)) - 5/(x+3)$

Now both denominators have something in common so we can combine them

$(9-5(x-3))/((x+3)(x-3))$

$(9-5x+15)/((x+3)(x-3))$

$((-5x)+24)/ ((x+3)(x-3))$ .................(5)

but $(-5x+24) = -(5x-24)$ ...............(6)

substituting (6) into (5) and rewriting the expression gives:

$- (5x-24)/(x^2-9)$

If you found this helpful please click on the thumbs up

How do you subtract 9/(x^2-9) - 5/ (x+3)9/(x^2-9) - 5/ (x+3)?