Math Quiz Due in 15 Minutes...10 points to first correct answer! Help please!!!?

Question

X- ___2___
x^2-9
___________
__1___
x-3

This is a double fraction question, i'm sorry but i did my best with what is available on my keyboard. The top half of the fraction is X minus (another fraction) 2 over x to the second power minus nine. this is all over the bottom half of the larger fraction which is 1 over x-3. Help!

P.S. I know that simplying the bottom half of the top equation x to the 2nd power minus 9 would make (x-3)(x+3) would give a common demoniator. I am unsure of actions after that.

Answer 1

To write this in text, use lots of brackets and spacing:

[x - (2 / (x^2-9))] / [1 / (x-3)]
Convert the division into a multiplication by inverting the second fraction:
= [x - (2 / (x^2-9))] . [(x-3) / 1]
Now we drop the division by 1 and multiply each part of the first bracket by (x-3):
= x(x-3) - (2 / (x^2-9)) (x-3)
= x^2 - 3x - (2 / ((x-3) (x+3))) (x-3)
= x^2 - 3x - 2 / (x+3).

Answer 2

1. Multiply the x by (x+3)(x-3)/(x +3)(x-3) to get a common denominator.

2. The 1/ (1 / (x-3)) just becomes (x - 3)

You now have:

(x - 3) ( x (x + 3) ( x - 3) - 2 )
--------------------------------------
(x + 3) ( x - 3)

3. Cancel out the common terms to get:

x(x - 3) - 2/(x + 3)


Don't know if more simplification than this is possible.