Solve for x 6/(2x-6)=3

$\frac{6}{2 x - 6} = 3$

Step 1

Factor each term.

Factor $2$ out of $2 x - 6$ .

Factor $2$ out of $2 x$ .

$\frac{6}{2 (x) - 6} = 3$

Factor $2$ out of $- 6$ .

$\frac{6}{2 x + 2 \cdot - 3} = 3$

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$\frac{6}{2 (x - 3)} = 3$

Reduce the expression $\frac{6}{2 (x - 3)}$ by cancelling the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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.

$x - 3, 1$

Remove parentheses.

$x - 3, 1$

The LCM of one and any expression is the expression.

$x - 3$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$3 = 3 (x - 3)$

Simplify the right side.

Apply the distributive property.

$3 = 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$3 = 3 x - 9$

Step 4

Solve the equation.

Rewrite the equation as $3 x - 9 = 3$ .

$3 x - 9 = 3$

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

Add $9$ to both sides of the equation.

$3 x = 3 + 9$

Add $3$ and $9$ .

$3 x = 12$

Divide each term in $3 x = 12$ by $3$ and simplify.

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

Divide $x$ by $1$ .

$x = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x = 4$

Solve for x 6/(2x-6)=3

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