Question

Solve for x: 5/x^2-4+2/x=2/x-2

Answer 1

`(5)/(x^2 - 4) + (2)/(x) = (2)/(x - 2)`

`(5)/((x + 2)(x - 2)) + (2)/(x) = (2)/(x - 2)`

`(5)/((x + 2)(x - 2)) * x(x + 2)(x - 2) + (2)/(x) * x(x + 2)(x - 2) = (2)/(x - 2) * x(x + 2)(x - 2)`

`5x + 2(x + 2)(x - 2) = 2x(x + 2)`

`5x + 2(x^2 - 4) = 2x^2 + 4x`

`5x + 2x^2 - 8 = 2x^2 + 4x`

`5x - 8 = 4x`

`x - 8 = 0`

`x = 8`

Now we look at the common denominator.

It is x(x + 2)(x - 2).

x cannot be zero, -2 or 2 because that would cause a zero in the denominator.

Since we get x = 8, and x = 8 does not have to be excluded from the domain, the answer is x = 8.

Answer: x = 8