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

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

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.

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

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

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

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

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

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

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

Combine 2x and x to get 3x.

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

Subtract 2 from 4 to get 2.

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

Subtract 3x from both sides.

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

Combine -x and -3x to get -4x.

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

Subtract x^{2} from both sides.

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

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

$$-4x=2$$

Divide both sides by -4.

$$x=\frac{2}{-4}$$

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

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