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

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

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-1,\left(x-1\right)\left(x+2\right).

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

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

$$2x+4=3$$

Subtract 4 from both sides.

$$2x=3-4$$

Subtract 4 from 3 to get -1.

$$2x=-1$$

Divide both sides by 2.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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