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

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

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of x^{2}-1,x+1,x-1.

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

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

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

Use the distributive property to multiply x^{2}-1 by 3.

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

Use the distributive property to multiply x-1 by 2.

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

Subtract 2 from -3 to get -5.

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

Use the distributive property to multiply x+1 by 3.

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

To find the opposite of 3x+3, find the opposite of each term.

$$3x^{2}-3x+1=3x^{2}-5+2x-3x-3$$

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

$$3x^{2}-3x+1=3x^{2}-5-x-3$$

Subtract 3 from -5 to get -8.

$$3x^{2}-3x+1=3x^{2}-8-x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-3x+1-3x^{2}=-8-x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-3x+1=-8-x$$

Add x to both sides.

$$-3x+1+x=-8$$

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

$$-2x+1=-8$$

Subtract 1 from both sides.

$$-2x=-8-1$$

Subtract 1 from -8 to get -9.

$$-2x=-9$$

Divide both sides by -2.

$$x=\frac{-9}{-2}$$

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{2}$$