Question

How do you solve `x/(x+4) - 4/(x-4) = (x^2+16)/(x^2-16)`?

Answer 1

NO SOLUTIONS!!!!

Explanation:

Consider as common denominator `x^2-16=(x-4)(x+4)`:
`(x(x-4)-4(x+4))/cancel((x^2-16))=(x^2+16)/cancel((x^2-16))`
`cancel(x^2)-4x-4x-16=cancel(x^2)+16`
`-8x=32`
`x=-4`
BUT this value cannot be accpeted because it makes the denominator of my original expression equal to ZERO!!!
So...NO real solutions!!!!