Find the difference: 2g/(g^2 - g - 6) -1/(g - 3).

I've been trying to figure this out on my own and by using Wolfram Alpha, but none of the answers I've come up with match the options.

Question

Find the difference: 2g/(g^2 - g - 6) -1/(g - 3). 

I've been trying to figure this out on my own and by using Wolfram Alpha, but none of the answers I've come up with match the options.

anonymous · Answer

$$\begin{align*}\frac{2g}{g^2-g-6}-\frac{1}{g-3}&=\frac{2g}{(g-3)(g+2)}-\frac{1}{g-3}\\
&=\frac{2g}{(g-3)(g+2)}-\frac{g+2}{(g-3)(g+2)}\\
&=\frac{2g-g-2}{(g-3)(g+2)}\\
&=\cdots
\end{align*}$$

drewbooks · Answer

That's the conclusion that I've come to as well, but it's not one of the options.

drewbooks · Answer

Can anyone come up with a solution that matches the options?

amistre64 · Answer

what are you coming up with?

drewbooks · Answer

The same thing that SithsAndGiggles got, but that can't be the answer that the test is looking for.

drewbooks · Answer

Are any of those answers even possible? I'm wondering if maybe the test is messed up.

anonymous · Answer

simplify the numerator

drewbooks · Answer

Simplify 2g and 1? I don't see how they could be simplified further. Do you mean something else?

anonymous · Answer

plug in numbers as g and see which one works

amistre64 · Answer

you said you got exactly what sith got .... and yet sith did not finish the process.  which leads one to think your not being as honest as you should be.

amistre64 · Answer

if you were to actually look at siths work, you would notice what needs to be finished up

drewbooks · Answer

What are you talking about? I got up to the point that Sith stopped at. Where can I go from there?

amistre64 · Answer

post for me what sith got up to, which would be were you are stopped at.

by writing it out it may jog something for you that is quite obvious ...

anonymous · Answer

it didnt give anser...

drewbooks · Answer

Actually, I did read Sith's reply too quickly - that's not as far as I made it. The answer I came up with is g - 2 / (g + 2)*(g - 3), but that's not one of the options.

drewbooks · Answer

I saw that lower part of what Sith got to and thought it was the same.

amistre64 · Answer

good, now we know the option must have g-2  up top

and the bottom is just the expanded form you started with ....

amistre64 · Answer

(g + 2)*(g - 3) = g^2 -g -6    ...

drewbooks · Answer

That's where I was having trouble, haha. Thank you.

drewbooks · Answer

I think I was overcomplicating it.

amistre64 · Answer

if it factors into 2 parts, itll go back together again :)

drewbooks · Answer

Thank you for the help!

amistre64 · Answer

good luck ;)