Solve -2/x+1+3/x-2=5/x^2-x-2

$$- \frac { 2 } { x + 1 } + \frac { 3 } { x - 2 } = \frac { 5 } { x ^ { 2 } - x - 2 }$$

Solve for x

$$x=-2$$

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.

$$-\left(x-2\right)\times 2+\left(x+1\right)\times 3=5$$

Use the distributive property to multiply x-2 by 2.

$$-\left(2x-4\right)+\left(x+1\right)\times 3=5$$

To find the opposite of 2x-4, find the opposite of each term.

$$-2x+4+\left(x+1\right)\times 3=5$$

Use the distributive property to multiply x+1 by 3.

$$-2x+4+3x+3=5$$

Combine -2x and 3x to get x.

$$x+4+3=5$$

Add 4 and 3 to get 7.

$$x+7=5$$

Subtract 7 from both sides.

$$x=5-7$$

Subtract 7 from 5 to get -2.

$$x=-2$$