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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right)\left(x+1\right), the least common multiple of x,x+1,x-1.

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

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

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

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

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

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

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

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

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

Subtract 2x^{2} from both sides.

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

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

$$-1-x=2x$$

Subtract 2x from both sides.

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

Combine -x and -2x to get -3x.

$$-1-3x=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-3x=1$$

Divide both sides by -3.

$$x=\frac{1}{-3}$$

Fraction \frac{1}{-3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$x=-\frac{1}{3}$$