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

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

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

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

$$x-1=x+2x-4$$

Combine x and 2x to get 3x.

$$x-1=3x-4$$

Subtract 3x from both sides.

$$x-1-3x=-4$$

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

$$-2x-1=-4$$

Add 1 to both sides.

$$-2x=-4+1$$

Add -4 and 1 to get -3.

$$-2x=-3$$

Divide both sides by -2.

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

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{2}$$