Solve for k -6/(2k-6)=1/3

$- \frac{6}{2 k - 6} = \frac{1}{3}$

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$- 6 \cdot 3 = (2 k - 6) \cdot 1$

Solve the equation for $k$ .

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Rewrite the equation as $(2 k - 6) \cdot 1 = - 6 \cdot 3$ .

$(2 k - 6) \cdot 1 = - 6 \cdot 3$

Simplify the equation.

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Multiply $2 k - 6$ by $1$ .

$2 k - 6 = - 6 \cdot 3$

Multiply $- 6$ by $3$ .

$2 k - 6 = - 18$

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

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Add $6$ to both sides of the equation.

$2 k = - 18 + 6$

Add $- 18$ and $6$ .

$2 k = - 12$

Divide each term by $2$ and simplify.

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Divide each term in $2 k = - 12$ by $2$ .

$\frac{2 k}{2} = \frac{- 12}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 k}{2} = \frac{- 12}{2}$

Divide $k$ by $1$ .

$k = \frac{- 12}{2}$

Divide $- 12$ by $2$ .

$k = - 6$

Solve for k -6/(2k-6)=1/3

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