Solve 3x-5/x-2=2-x+1/x-2

$$\frac { 3 x - 5 } { x - 2 } = 2 - \frac { x + 1 } { x - 2 }$$

Solve for x

$$x=0$$

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.

$$3x-5=\left(x-2\right)\times 2-\left(x+1\right)$$

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

$$3x-5=2x-4-\left(x+1\right)$$

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

$$3x-5=2x-4-x-1$$

Combine 2x and -x to get x.

$$3x-5=x-4-1$$

Subtract 1 from -4 to get -5.

$$3x-5=x-5$$

Subtract x from both sides.

$$3x-5-x=-5$$

Combine 3x and -x to get 2x.

$$2x-5=-5$$

Add 5 to both sides.

$$2x=-5+5$$

Add -5 and 5 to get 0.

$$2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 2 is not equal to 0, x must be equal to 0.

$$x=0$$