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

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

$$\left(x-4\right)\left(x-2\right)=\left(x+2\right)\left(x+8\right)$$

Use the distributive property to multiply x-4 by x-2 and combine like terms.

$$x^{2}-6x+8=\left(x+2\right)\left(x+8\right)$$

Use the distributive property to multiply x+2 by x+8 and combine like terms.

$$x^{2}-6x+8=x^{2}+10x+16$$

Subtract x^{2} from both sides.

$$x^{2}-6x+8-x^{2}=10x+16$$

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

$$-6x+8=10x+16$$

Subtract 10x from both sides.

$$-6x+8-10x=16$$

Combine -6x and -10x to get -16x.

$$-16x+8=16$$

Subtract 8 from both sides.

$$-16x=16-8$$

Subtract 8 from 16 to get 8.

$$-16x=8$$

Divide both sides by -16.

$$x=\frac{8}{-16}$$

Reduce the fraction \frac{8}{-16} to lowest terms by extracting and canceling out 8.

$$x=-\frac{1}{2}$$