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

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

Solve for x

$$x=-6$$

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-2,x+2,x-1.

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

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

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

Subtract 3 from 1 to get -2.

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

Use the distributive property to multiply x+2 by 5.

$$-2+3x=5x+10$$

Subtract 5x from both sides.

$$-2+3x-5x=10$$

Combine 3x and -5x to get -2x.

$$-2-2x=10$$

Add 2 to both sides.

$$-2x=10+2$$

Add 10 and 2 to get 12.

$$-2x=12$$

Divide both sides by -2.

$$x=\frac{12}{-2}$$

Divide 12 by -2 to get -6.

$$x=-6$$