Solve the equation. (If possible)

5/x-5 + 1/x+5 = 2/x^2-25

Question

Solve the equation. (If possible)

5/x-5 + 1/x+5 = 2/x^2-25

anonymous · Answer

Start by multiplying everything by x^2

hero · Answer

Now just wait one minute...I don't think multiplying everything by x^2 is the best way to go.

anonymous · Answer

ahhh, i was reading the problem differently

hero · Answer

Here's what we should probably do instead:

1. Make sure the denominators are factored:

$$\frac{5}{x-5} + \frac{1}{x+5} = \frac{2}{(x+5)(x-5)}$$

anonymous · Answer

Ok I understand that

anonymous · Answer

Should I get the denominators to be the same?

hero · Answer

Well, in this case the next step would be to multiply both sides by (x-5)

hero · Answer

What would you end up with if you did that?

anonymous · Answer

why would i multiply both by x-5?

hero · Answer

Because, if you did that, you would get this:

$$5 - \frac{x-5}{x+5} = \frac{2}{x+5}$$

hero · Answer

Now all you would have to do after that is add $\large \frac{x-5}{x+5}$ to both sides.

anonymous · Answer

Thank you!

hero · Answer

Oh no...you can't get off that easy. You're not done until you tell me what x equals :P

hero · Answer

If you get it right, I'll give you a medal.