Algebra Examples

$\frac{12 k^{2} - 54 k}{6 k} \cdot \frac{6}{81 - 18 k}$

Step 1

Simplify terms.

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Step 1.1

Factor $6 k$ out of $12 k^{2} - 54 k$ .

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Step 1.1.1

Factor $6 k$ out of $12 k^{2}$ .

$\frac{6 k (2 k) - 54 k}{6 k} \cdot \frac{6}{81 - 18 k}$

Step 1.1.2

Factor $6 k$ out of $- 54 k$ .

$\frac{6 k (2 k) + 6 k (- 9)}{6 k} \cdot \frac{6}{81 - 18 k}$

Step 1.1.3

Factor $6 k$ out of $6 k (2 k) + 6 k (- 9)$ .

$\frac{6 k (2 k - 9)}{6 k} \cdot \frac{6}{81 - 18 k}$

Step 1.2

Factor $9$ out of $81 - 18 k$ .

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Step 1.2.1

Factor $9$ out of $81$ .

$\frac{6 k (2 k - 9)}{6 k} \cdot \frac{6}{9 (9) - 18 k}$

Step 1.2.2

Factor $9$ out of $- 18 k$ .

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

Step 1.2.3

Factor $9$ out of $9 (9) + 9 (- 2 k)$ .

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

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $6 k (2 k - 9)$ .

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

Step 1.3.2

Factor $3$ out of $9 (9 - 2 k)$ .

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

Step 1.3.3

Cancel the common factor.

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

Step 1.3.4

Rewrite the expression.

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

Step 1.4

Cancel the common factor of $6$ .

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Step 1.4.1

Factor $6$ out of $6 k$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

$\frac{2 k (2 k - 9)}{k} \cdot \frac{1}{3 (9 - 2 k)}$

Step 1.5

Multiply $\frac{2 k (2 k - 9)}{k}$ by $\frac{1}{3 (9 - 2 k)}$ .

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

Step 1.6

Cancel the common factor of $k$ .

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Step 1.6.1

Cancel the common factor.

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

Step 1.6.2

Rewrite the expression.

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

Step 1.7

Cancel the common factor of $2 k - 9$ and $9 - 2 k$ .

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Step 1.7.1

Factor $- 1$ out of $2 k$ .

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

Step 1.7.2

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{2 (- (- 2 k) - 1 (9))}{3 (9 - 2 k)}$

Step 1.7.3

Factor $- 1$ out of $- (- 2 k) - 1 (9)$ .

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

Step 1.7.4

Rewrite $- (- 2 k + 9)$ as $- 1 (- 2 k + 9)$ .

$\frac{2 (- 1 (- 2 k + 9))}{3 (9 - 2 k)}$

Step 1.7.5

Reorder terms.

$\frac{2 (- 1 (- 2 k + 9))}{3 (- 2 k + 9)}$

Step 1.7.6

Cancel the common factor.

$\frac{2 (- 1 (- 2 k + 9))}{3 (- 2 k + 9)}$

Step 1.7.7

Rewrite the expression.

$\frac{2 \cdot (- 1)}{3}$

Step 2

Multiply $2$ by $- 1$ .

$\frac{- 2}{3}$

Step 3

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$