Solve x/x^2+x-2-3/x^2+2x-3=x/x^2+5x+6

$$\frac { x } { x ^ { 2 } + x - 2 } - \frac { 3 } { x ^ { 2 } + 2 x - 3 } = \frac { x } { x ^ { 2 } + 5 x + 6 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,-2,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+2\right)\left(x+3\right), the least common multiple of x^{2}+x-2,x^{2}+2x-3,x^{2}+5x+6.

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

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

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

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

$$x^{2}+3x-\left(3x+6\right)=\left(x-1\right)x$$

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

$$x^{2}+3x-3x-6=\left(x-1\right)x$$

Combine 3x and -3x to get 0.

$$x^{2}-6=\left(x-1\right)x$$

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

$$x^{2}-6=x^{2}-x$$

Subtract x^{2} from both sides.

$$x^{2}-6-x^{2}=-x$$

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

$$-6=-x$$

Swap sides so that all variable terms are on the left hand side.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$