Question

x/x+7 - 7/x-7 = x^2+49/x^2-49

Answer 1

My first step would be to find a common denominator for those fractions so I could add them. What would that look like?

Answer 2

(x+7) (x-7)?

Answer 3

That's the common denominator, yep! So how can you use that to add the fractions?

Answer 4

u use them as the base?

Answer 5

Yep, so for example, the first fraction will go from:
\[\frac{x}{x+7} \Rightarrow \frac{?}{(x+7)(x-7)}\]What goes in place of the ?

Answer 6

will it be (x+7) +x-7 after factoring x^2+49

Answer 7

Unfortunately, x^2+49 cannot be factored.

Answer 8

What goes in place of that ? from before?

Answer 9

x-7

Answer 10

Close! Don't forget that there was an x there already.

Answer 11

7?

Answer 12

\[\frac{x}{x+7}=\frac{x}{x+7}\times\frac{x-7}{x-7}\]

Answer 13

so will that be x^2-7x/(x+7) (x-7)

Answer 14

x/x+7 - 7/x-7
= x (x-7) - 7 (x + 7) / (x^2 - 49 )
= x^2 - 14x + 49 / (x^2 - 49 )
Thus [x^2 - 14x + 49 / (x^2 - 49 ) ]= [(x^2 + 49) /(x^2 - 49 )]
-> -14x / (x^2 - 49 )

Answer 15

so is the answer -14x/x^2-49

Answer 16

Yes!

Answer 17

thx so much

Answer 18

I'm glad I can help!

Answer 19

Once you have that, you can set it equal to the other side of the equation, and solve for x.