Solve x+2/x-2-1=8/x^2-4

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x-2,x^{2}-4.

$$\left(x+2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

$$\left(x+2\right)^{2}+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$x^{2}+4x+4+\left(x-2\right)\left(x+2\right)\left(-1\right)=8$$

Use the distributive property to multiply x-2 by x+2 and combine like terms.

$$x^{2}+4x+4+\left(x^{2}-4\right)\left(-1\right)=8$$

Use the distributive property to multiply x^{2}-4 by -1.

$$x^{2}+4x+4-x^{2}+4=8$$

Combine x^{2} and -x^{2} to get 0.

$$4x+4+4=8$$

Add 4 and 4 to get 8.

$$4x+8=8$$

Subtract 8 from both sides.

$$4x=8-8$$

Subtract 8 from 8 to get 0.

$$4x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 4 is not equal to 0, x must be equal to 0.

$$x=0$$