Solve x/x-1-1=1/(x-1)(x+1)

$$\frac { x } { x - 1 } - 1 = \frac { 1 } { ( x - 1 ) ( x + 1 ) }$$

Solve for x

$$x=0$$

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,\left(x-1\right)\left(x+1\right).

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

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

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

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

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

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

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

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

$$x+1=1$$

Subtract 1 from both sides.

$$x=1-1$$

Subtract 1 from 1 to get 0.

$$x=0$$