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

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

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right), the least common multiple of x-1,3.

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

Multiply 3 and \frac{2}{3} to get 2.

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

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

$$3=2x-2+3\times 2$$

Multiply 3 and 2 to get 6.

$$3=2x-2+6$$

Add -2 and 6 to get 4.

$$3=2x+4$$

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

$$2x+4=3$$

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.

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