Solve 2/x^2-9+5/x-3=3/x+3

$$\frac { 2 } { x ^ { 2 } - 9 } + \frac { 5 } { x - 3 } = \frac { 3 } { x + 3 }$$

Solve for x

$$x=-13$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right), the least common multiple of x^{2}-9,x-3,x+3.

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

Use the distributive property to multiply x+3 by 5.

$$2+5x+15=\left(x-3\right)\times 3$$

Add 2 and 15 to get 17.

$$17+5x=\left(x-3\right)\times 3$$

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

$$17+5x=3x-9$$

Subtract 3x from both sides.

$$17+5x-3x=-9$$

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

$$17+2x=-9$$

Subtract 17 from both sides.

$$2x=-9-17$$

Subtract 17 from -9 to get -26.

$$2x=-26$$

Divide both sides by 2.

$$x=\frac{-26}{2}$$

Divide -26 by 2 to get -13.

$$x=-13$$