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

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

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

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-1,2+x.

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

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

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

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

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

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

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

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

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

Combine 2x and -x to get x.

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

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

$$x+2=3x-3$$

Subtract 3x from both sides.

$$x+2-3x=-3$$

Combine x and -3x to get -2x.

$$-2x+2=-3$$

Subtract 2 from both sides.

$$-2x=-3-2$$

Subtract 2 from -3 to get -5.

$$-2x=-5$$

Divide both sides by -2.

$$x=\frac{-5}{-2}$$

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{2}$$