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

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

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

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.

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

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

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

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

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

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

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

Subtract 2 from -3 to get -5.

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

To find the opposite of x+1, find the opposite of each term.

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

Combine 2x and -x to get x.

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

Subtract 1 from -5 to get -6.

$$3x^{2}-3x+1=3x^{2}-6+x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-3x+1-3x^{2}=-6+x$$

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

$$-3x+1=-6+x$$

Subtract x from both sides.

$$-3x+1-x=-6$$

Combine -3x and -x to get -4x.

$$-4x+1=-6$$

Subtract 1 from both sides.

$$-4x=-6-1$$

Subtract 1 from -6 to get -7.

$$-4x=-7$$

Divide both sides by -4.

$$x=\frac{-7}{-4}$$

Fraction \frac{-7}{-4} can be simplified to \frac{7}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{4}$$