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

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

Solve for x

$$x=4$$

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-3,x^{2}-9.

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

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

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

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}-3x+x^{2}+2x-3=2x^{2}-2x+1$$

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

$$2x^{2}-3x+2x-3=2x^{2}-2x+1$$

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

$$2x^{2}-x-3=2x^{2}-2x+1$$

Subtract 2x^{2} from both sides.

$$2x^{2}-x-3-2x^{2}=-2x+1$$

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

$$-x-3=-2x+1$$

Add 2x to both sides.

$$-x-3+2x=1$$

Combine -x and 2x to get x.

$$x-3=1$$

Add 3 to both sides.

$$x=1+3$$

Add 1 and 3 to get 4.

$$x=4$$