Question

Solve the valid solutions of the following equations providing your values for some of them. Write your answers in solution set form. Identify the extraneous solution, if there is.

x 1 8

------- - -------- = ---------

x + 2 x - 2 x^2 - 4

Answer 1

$$\dfrac{x}{x+2}-\dfrac{1}{x-2}=\dfrac{8}{x^2-4}$$

$$x(x-2)-(x+2)=8, x \not=\pm2$$

$$x^2-2x-x-2-8=0$$

$$x^2-3x-10=0$$

$$(x+2)(x-5)=0$$

$$x_1=-2, x_2=5$$

But $x \not=\pm2$

The solution $x=-2$ is extraneous and is not valid.

$\{5\}$