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

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

Solve for x

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right), the least common multiple of x-4,2x-8,2.

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

Use the distributive property to multiply 2 by x+4.

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

Use the distributive property to multiply x-4 by x.

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

Subtract x^{2} from both sides.

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

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

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

Add 4x to both sides.

$$2x+8+4x=0$$

Combine 2x and 4x to get 6x.

$$6x+8=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$6x=-8$$

Divide both sides by 6.

$$x=\frac{-8}{6}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{4}{3}$$