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

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right)\left(x+2\right), the least common multiple of x,x-1,x+2.

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

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

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

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

$$2x^{2}+2x-4-x\left(x+2\right)=x\left(x-1\right)$$

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

$$2x^{2}+2x-4-\left(x^{2}+2x\right)=x\left(x-1\right)$$

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

$$2x^{2}+2x-4-x^{2}-2x=x\left(x-1\right)$$

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

$$x^{2}+2x-4-2x=x\left(x-1\right)$$

Combine 2x and -2x to get 0.

$$x^{2}-4=x\left(x-1\right)$$

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

$$x^{2}-4=x^{2}-x$$

Subtract x^{2} from both sides.

$$x^{2}-4-x^{2}=-x$$

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

$$-4=-x$$

Swap sides so that all variable terms are on the left hand side.

$$-x=-4$$

Multiply both sides by -1.

$$x=4$$