Solve x-1/x+1-2x-1/2x+1=0

$$\frac{ x-1 }{ x+1 } - \frac{ 2x-1 }{ 2x+1 } =0$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$\left(2x+1\right)\left(x-1\right)-\left(x+1\right)\left(2x-1\right)=0$$

Use the distributive property to multiply 2x+1 by x-1 and combine like terms.

$$2x^{2}-x-1-\left(x+1\right)\left(2x-1\right)=0$$

Use the distributive property to multiply x+1 by 2x-1 and combine like terms.

$$2x^{2}-x-1-\left(2x^{2}+x-1\right)=0$$

To find the opposite of 2x^{2}+x-1, find the opposite of each term.

$$2x^{2}-x-1-2x^{2}-x+1=0$$

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

$$-x-1-x+1=0$$

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

$$-2x-1+1=0$$

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.

$$x=0$$