Solve x/x+1-1/x-1=1

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

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,x-1.

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

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

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

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

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

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

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

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.

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

Subtract x^{2} from both sides.

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

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

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

Add 1 to both sides.

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

Add -1 and 1 to get 0.

$$-2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.

$$x=0$$