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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+1\right), the least common multiple of x+1,x-2,x^{2}-x-2.

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

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

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

Use the distributive property to multiply x+1 by x+8 and combine like terms.

$$4x-x^{2}-4+x^{2}+9x+8=4-x$$

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

$$4x-4+9x+8=4-x$$

Combine 4x and 9x to get 13x.

$$13x-4+8=4-x$$

Add -4 and 8 to get 4.

$$13x+4=4-x$$

Add x to both sides.

$$13x+4+x=4$$

Combine 13x and x to get 14x.

$$14x+4=4$$

Subtract 4 from both sides.

$$14x=4-4$$

Subtract 4 from 4 to get 0.

$$14x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 14 is not equal to 0, x must be equal to 0.

$$x=0$$