# Thread: How do I subtract and simplify this?

1. ## How do I subtract and simplify this?

Hi everyone, this is my first post and I don't really know how things work around here, but I'll ask my question.

I'm in Algebra 2 and I'm having trouble finding how to do this particular problem in my textbook:

Subtract, simplify, and note domain exclusion:

(6/x^2-9)-(1/x-3)

I know that I should probably factor the denominator of 6/x^2-9 because it's a difference of squares, but I have no idea how to make them both have like denominators in order to subtract! I also think that the exclusion is -3 but I'm not completely sure of that either.

I know for a fact that the domain is (-∞, 3)∪(3,∞)

Help as soon as possible would be greatly appreciated! (my test corrections are actually due tomorrow )

-Lissy

2. Originally Posted by Numbers_Hurt

Subtract, simplify, and note domain exclusion:

(6/x^2-9)-(1/x-3)

I know that I should probably factor the denominator of 6/x^2-9 because it's a difference of squares, but I have no idea how to make them both have like denominators in order to subtract! I also think that the exclusion is -3 but I'm not completely sure of that either.

I know for a fact that the domain is (-∞, 3)∪(3,∞)
$\displaystyle \frac{6}{(x+3)(x-3)} - \frac{1}{x-3}$

$\displaystyle \frac{6}{(x+3)(x-3)} - \frac{x+3}{(x+3)(x-3)}$

$\displaystyle \frac{6 - (x+3)}{(x+3)(x-3)}$

you finish

btw, here is how to use parentheses properly to make your post clear ...

6/(x^2-9) - 1/(x-3)

also, I don't agree with your domain.

3. Thanks for responding so quickly!

can you cancel the x+3 so you are left with

5/(x-3) ??

and do you agree with the exclusions? I feel a bit stupid right about now.....

4. Originally Posted by Numbers_Hurt
Thanks for responding so quickly!

can you cancel the x+3 so you are left with ... no, it's not a factor of the numerator

5/(x-3) ??

and do you agree with the exclusions? I feel a bit stupid right about now.....
$\displaystyle \frac{6 - (x+3)}{(x+3)(x-3)}$

$\displaystyle \frac{3-x}{(x+3)(x-3)}$

$\displaystyle -\frac{1}{x+3}$