Solve x^2-9/x^2-4=x-3/x+2

$$\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 } = \frac { x - 3 } { x + 2 }$$

Solve for x

$$x=3$$

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.

$$x^{2}-9=\left(x-2\right)\left(x-3\right)$$

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

$$x^{2}-9=x^{2}-5x+6$$

Subtract x^{2} from both sides.

$$x^{2}-9-x^{2}=-5x+6$$

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

$$-9=-5x+6$$

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

$$-5x+6=-9$$

Subtract 6 from both sides.

$$-5x=-9-6$$

Subtract 6 from -9 to get -15.

$$-5x=-15$$

Divide both sides by -5.

$$x=\frac{-15}{-5}$$

Divide -15 by -5 to get 3.

$$x=3$$