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

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

Solve for x

$$x=3$$

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-1,x+1,x.

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

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

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

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

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

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

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

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

Combine x and -2x to get -x.

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

Use the distributive property to multiply x^{2}-1 by 3.

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

Subtract 3x^{2} from both sides.

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

Combine 3x^{2} and -3x^{2} to get 0.

$$-x=-3$$

Multiply both sides by -1.

$$x=3$$