Solve 4/x^2-4+x+3/x-2=x-1/x+2

$$\frac { 4 } { x ^ { 2 } - 4 } + \frac { x + 3 } { x - 2 } = \frac { x - 1 } { x + 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x^{2}-4,x-2,x+2.

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

Use the distributive property to multiply x+2 by x+3 and combine like terms.

$$4+x^{2}+5x+6=\left(x-2\right)\left(x-1\right)$$

Add 4 and 6 to get 10.

$$10+x^{2}+5x=\left(x-2\right)\left(x-1\right)$$

Use the distributive property to multiply x-2 by x-1 and combine like terms.

$$10+x^{2}+5x=x^{2}-3x+2$$

Subtract x^{2} from both sides.

$$10+x^{2}+5x-x^{2}=-3x+2$$

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

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

Add 3x to both sides.

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

Combine 5x and 3x to get 8x.

$$10+8x=2$$

Subtract 10 from both sides.

$$8x=2-10$$

Subtract 10 from 2 to get -8.

$$8x=-8$$

Divide both sides by 8.

$$x=\frac{-8}{8}$$

Divide -8 by 8 to get -1.

$$x=-1$$