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

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

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x+2 by 3.

$$x-1-\left(3x+6\right)=3$$

To find the opposite of 3x+6, find the opposite of each term.

$$x-1-3x-6=3$$

Combine x and -3x to get -2x.

$$-2x-1-6=3$$

Subtract 6 from -1 to get -7.

$$-2x-7=3$$

Add 7 to both sides.

$$-2x=3+7$$

Add 3 and 7 to get 10.

$$-2x=10$$

Divide both sides by -2.

$$x=\frac{10}{-2}$$

Divide 10 by -2 to get -5.

$$x=-5$$