Question

(x)/(x+4)-(4)/(x-4)=(x^2+16)/(x^2-16)

Answer 1

let me rewrite for clarity

Answer 2

\[\frac{x}{(x+4)}-\frac{4}{(x-4)}=\frac{(x^2+16)}{(x^2-16)}\]

Answer 3

Do you know what's special about x^2-16?

Answer 4

DIFFERENCE OF TWO PERFECT SQUARES

Answer 5

So that becomes (x+4)(x-4)

Answer 6

Now say that we wanted to get rid of the denominators so this problem is easier. We can multiply the whole equation by (x+4)(x-4), because that takes care of all the denomointors

Answer 7

it becomes...

Answer 8

\[x(x-4)-4(x+4)=x^2+16\]

Answer 9

Do you see how I got that?

Answer 10

@slaven? :P