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

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

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,0,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right)x^{2}, the least common multiple of x^{2}-3x,x^{2}-9,x^{2}.

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

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

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

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

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

Use the distributive property to multiply x^{2}+3x by 3.

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

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$4x^{2}+3x+9x=x^{2}\times 2+\left(x^{2}-9\right)\times 2$$

Combine 3x and 9x to get 12x.

$$4x^{2}+12x=x^{2}\times 2+\left(x^{2}-9\right)\times 2$$

Use the distributive property to multiply x^{2}-9 by 2.

$$4x^{2}+12x=x^{2}\times 2+2x^{2}-18$$

Combine x^{2}\times 2 and 2x^{2} to get 4x^{2}.

$$4x^{2}+12x=4x^{2}-18$$

Subtract 4x^{2} from both sides.

$$4x^{2}+12x-4x^{2}=-18$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x=-18$$

Divide both sides by 12.

$$x=\frac{-18}{12}$$

Reduce the fraction \frac{-18}{12} to lowest terms by extracting and canceling out 6.

$$x=-\frac{3}{2}$$