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

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Combine 2x and x to get 3x.

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

Subtract 2 from -2 to get -4.

$$3x-4+x^{2}=\left(x+2\right)x$$

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

$$3x-4+x^{2}=x^{2}+2x$$

Subtract x^{2} from both sides.

$$3x-4+x^{2}-x^{2}=2x$$

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

$$3x-4=2x$$

Subtract 2x from both sides.

$$3x-4-2x=0$$

Combine 3x and -2x to get x.

$$x-4=0$$

Add 4 to both sides. Anything plus zero gives itself.

$$x=4$$