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

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

Solve for x

$$x=2$$

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-1,x^{2}-1.

$$\left(x+1\right)x=3+\left(x-1\right)\left(x+1\right)$$

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

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

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

Subtract 1 from 3 to get 2.

$$x^{2}+x=2+x^{2}$$

Subtract x^{2} from both sides.

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

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

$$x=2$$