Solve for the following equation for x. 2/x^2-4 = x-3/x+2?

Question

2/x^2-4
=
x-3/x+2

Please explain steps...

Answer 1

I'm assuming it's bracketed
2/(x^2-4) = (x-3)/(x+2)
2/((x-2)(x+2) = (x-3)/(x+2)
2/(x-2) = x-3
2 = (x-2)(x-3)
2 = x^2 - 5x + 6
x^2 - 5x + 4 = 0
(x - 1)(x - 4) = 0 - factorise the quadratic equation...
x = 1, x = 4

So x is either 1 or 4.

Answer 2

I will assume you mean 2/(x^2-4) = (x-3)/(x+2)

you can cross multiply to get:

2(x+2) = (x-3)(x^2-4)

Then factor to get:

2(x+2) = (x-3)(x+2)(x-2)

divide by (x+2) and foil to get

2=x^2 - 5x + 6

x^2 - 5x + 4 = 0

(x-4)(x-1) = 0

x=4 or x=1

Answer 3

2 / (x - 2).(x + 2) = (x - 3) / (x + 2)
2 = (x - 3).(x - 2)
x² - 5x + 6 = 2
x² - 5x + 4 = 0
(x - 4).(x - 1) = 0
x = 1 , x = 4