Solve 2x-9/x-3-5x-1/x^2-9=2x+6/x+3

$$\frac{ 2x-9 }{ x-3 } - \frac{ 5x-1 }{ { x }^{ 2 } -9 } = \frac{ 2x+6 }{ x+3 }$$

Solve for x

$$x=-1$$

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-3,x^{2}-9,x+3.

$$\left(x+3\right)\left(2x-9\right)-\left(5x-1\right)=\left(x-3\right)\left(2x+6\right)$$

Use the distributive property to multiply x+3 by 2x-9 and combine like terms.

$$2x^{2}-3x-27-\left(5x-1\right)=\left(x-3\right)\left(2x+6\right)$$

To find the opposite of 5x-1, find the opposite of each term.

$$2x^{2}-3x-27-5x+1=\left(x-3\right)\left(2x+6\right)$$

Combine -3x and -5x to get -8x.

$$2x^{2}-8x-27+1=\left(x-3\right)\left(2x+6\right)$$

Add -27 and 1 to get -26.

$$2x^{2}-8x-26=\left(x-3\right)\left(2x+6\right)$$

Use the distributive property to multiply x-3 by 2x+6 and combine like terms.

$$2x^{2}-8x-26=2x^{2}-18$$

Subtract 2x^{2} from both sides.

$$2x^{2}-8x-26-2x^{2}=-18$$

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

$$-8x-26=-18$$

Add 26 to both sides.

$$-8x=-18+26$$

Add -18 and 26 to get 8.

$$-8x=8$$

Divide both sides by -8.

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

Divide 8 by -8 to get -1.

$$x=-1$$