Solve for x -3=3/(x-2)

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

Rewrite the equation as $\frac{3}{x - 2} = - 3$ .

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

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 2, 1$

Remove parentheses.

$x - 2, 1$

The LCM of one and any expression is the expression.

$x - 2$

Multiply each term in $\frac{3}{x - 2} = - 3$ by $x - 2$ to eliminate the fractions.

Multiply each term in $\frac{3}{x - 2} = - 3$ by $x - 2$ .

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

Simplify the left side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 = - 3 (x - 2)$

Simplify the right side.

Apply the distributive property.

$3 = - 3 x - 3 \cdot - 2$

Multiply $- 3$ by $- 2$ .

$3 = - 3 x + 6$

Solve the equation.

Rewrite the equation as $- 3 x + 6 = 3$ .

$- 3 x + 6 = 3$

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$- 3 x = 3 - 6$

Subtract $6$ from $3$ .

$- 3 x = - 3$

Divide each term in $- 3 x = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 3$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x = 1$