Simplify 6/(6k-9)-6/2

$\frac{6}{6 k - 9} - \frac{6}{2}$

Step 1

Simplify each term.

Cancel the common factor of $6$ and $6 k - 9$ .

Factor $3$ out of $6$ .

$\frac{3 (2)}{6 k - 9} - \frac{6}{2}$

Cancel the common factors.

Factor $3$ out of $6 k$ .

$\frac{3 (2)}{3 (2 k) - 9} - \frac{6}{2}$

Factor $3$ out of $- 9$ .

$\frac{3 \cdot 2}{3 (2 k) + 3 \cdot - 3} - \frac{6}{2}$

Factor $3$ out of $3 (2 k) + 3 (- 3)$ .

$\frac{3 (2)}{3 (2 k - 3)} - \frac{6}{2}$

Cancel the common factor.

$\frac{3 \cdot 2}{3 (2 k - 3)} - \frac{6}{2}$

Rewrite the expression.

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

Divide $6$ by $2$ .

$\frac{2}{2 k - 3} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$\frac{2}{2 k - 3} - 3$

Step 2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2 k - 3}{2 k - 3}$ .

$\frac{2}{2 k - 3} - 3 \cdot \frac{2 k - 3}{2 k - 3}$

Step 3

Simplify terms.

Combine $- 3$ and $\frac{2 k - 3}{2 k - 3}$ .

$\frac{2}{2 k - 3} + \frac{- 3 (2 k - 3)}{2 k - 3}$

Combine the numerators over the common denominator.

$\frac{2 - 3 (2 k - 3)}{2 k - 3}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{2 - 3 (2 k) - 3 \cdot - 3}{2 k - 3}$

Multiply $2$ by $- 3$ .

$\frac{2 - 6 k - 3 \cdot - 3}{2 k - 3}$

Multiply $- 3$ by $- 3$ .

$\frac{2 - 6 k + 9}{2 k - 3}$

Add $2$ and $9$ .

$\frac{- 6 k + 11}{2 k - 3}$

Step 5

Simplify with factoring out.

Factor $- 1$ out of $- 6 k$ .

$\frac{- (6 k) + 11}{2 k - 3}$

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{- (6 k) - 1 (- 11)}{2 k - 3}$

Factor $- 1$ out of $- (6 k) - 1 (- 11)$ .

$\frac{- (6 k - 11)}{2 k - 3}$

Simplify the expression.

Rewrite $- (6 k - 11)$ as $- 1 (6 k - 11)$ .

$\frac{- 1 (6 k - 11)}{2 k - 3}$

Move the negative in front of the fraction.

$- \frac{6 k - 11}{2 k - 3}$

Simplify 6/(6k-9)-6/2

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