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

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x-1, the least common multiple of 2x-1,1-2x.

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

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

$$x+2=4x-2$$

Subtract 4x from both sides.

$$x+2-4x=-2$$

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

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

Subtract 2 from both sides.

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

Subtract 2 from -2 to get -4.

$$-3x=-4$$

Divide both sides by -3.

$$x=\frac{-4}{-3}$$

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{3}$$