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

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

Solve for x

$$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

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.

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

To find the opposite of x-1, find the opposite of each term.

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

Add 3 and 1 to get 4.

$$4-x=2\left(x-2\right)$$

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

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

Subtract 2x from both sides.

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

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

$$4-3x=-4$$

Subtract 4 from both sides.

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

Subtract 4 from -4 to get -8.

$$-3x=-8$$

Divide both sides by -3.

$$x=\frac{-8}{-3}$$

Fraction \frac{-8}{-3} can be simplified to \frac{8}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{8}{3}$$