Question

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

Answer 1

$\dfrac{5}{x^2 - 4} + \dfrac{2}{x} = \dfrac{2}{x - 2}$

$\dfrac{5}{(x + 2)(x - 2)} + \dfrac{2}{x} = \dfrac{2}{x - 2}$

$\dfrac{5}{(x + 2)(x - 2)} \times x(x + 2)(x - 2) + \dfrac{2}{x} \times x(x + 2)(x - 2) = \dfrac{2}{x - 2} \times x(x + 2)(x - 2)$

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

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

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

$5x - 8 = 4x$

$x - 8 = 0$

$x = 8$

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