Question

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Answer 1

First, write out the problem:
\[\frac{-3x}{x^2-9} + \frac{4}{2x-6}\]

Answer 2

Factor the denominator of each fraction:
\[\frac{-3x}{(x+3)(x-3)}+\frac{4}{2*(x-3)}\]

Answer 3

Simplify:
\[\frac{-3x}{(x+3)(x-3)}+\frac{2}{(x-3)}\]

Answer 4

Multiply the fraction on the left by a clever form of 1:
\[\frac{-3x}{(x+3)(x-3)}+\frac{2}{(x-3)} * \frac{(x+3)}{(x+3)}\]

Answer 5

Simplify:
\[\frac{-3x}{(x+3)(x-3)}+\frac{2x+6}{(x+3)(x-3)}\]

Answer 6

Think you can take it from here?

Answer 7

Do we take out the common factors now?? @LukeBlueFive

Answer 8

I'd add the two fractions together first, personally, since we're trying to simplify the sum.

Answer 9

Ahh okay. It's new to me. I'll try adding now.

Answer 10

Honestly, taking out common factors always looks incredibly tempting to me too.

Answer 11

Same here! So I got
6-x/(x-3)(x + 3)

Is that right?

Answer 12

That looks right to me. Now I'd multiply the denominator's factor together.

Answer 13

It'll be at least somewhat simpler then, at least.

Answer 14

Would it be 6-x/x^2-9?

Answer 15

That looks right to me.

Answer 16

And that's it? :o

Answer 17

I'm not sure how else you could simplify it, but if you have any ideas, go for it!