Answer to Question #194279 in Algebra for kmy

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.

$\{5\}$