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

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

Solve for x

$$x=3$$

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.

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

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

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

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

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

Use the distributive property to multiply 2x-2 by x.

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

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

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

Combine x and -2x to get -x.

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

Use the distributive property to multiply 3 by x-1.

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

Use the distributive property to multiply 3x-3 by x+1 and combine like terms.

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

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.

$$x=3$$