Basic Math Examples

$\frac{28 k^{2} - 4 k^{3}}{k - 6} \div \frac{4 k^{3} - 28 k^{2}}{k - 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{28 k^{2} - 4 k^{3}}{k - 6} \cdot \frac{k - 4}{4 k^{3} - 28 k^{2}}$

Step 2

Factor $4 k^{2}$ out of $28 k^{2} - 4 k^{3}$ .

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Step 2.1

Factor $4 k^{2}$ out of $28 k^{2}$ .

$\frac{4 k^{2} (7) - 4 k^{3}}{k - 6} \cdot \frac{k - 4}{4 k^{3} - 28 k^{2}}$

Step 2.2

Factor $4 k^{2}$ out of $- 4 k^{3}$ .

$\frac{4 k^{2} (7) + 4 k^{2} (- k)}{k - 6} \cdot \frac{k - 4}{4 k^{3} - 28 k^{2}}$

Step 2.3

Factor $4 k^{2}$ out of $4 k^{2} (7) + 4 k^{2} (- k)$ .

$\frac{4 k^{2} (7 - k)}{k - 6} \cdot \frac{k - 4}{4 k^{3} - 28 k^{2}}$

Step 3

Factor $4 k^{2}$ out of $4 k^{3} - 28 k^{2}$ .

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Step 3.1

Factor $4 k^{2}$ out of $4 k^{3}$ .

$\frac{4 k^{2} (7 - k)}{k - 6} \cdot \frac{k - 4}{4 k^{2} (k) - 28 k^{2}}$

Step 3.2

Factor $4 k^{2}$ out of $- 28 k^{2}$ .

$\frac{4 k^{2} (7 - k)}{k - 6} \cdot \frac{k - 4}{4 k^{2} (k) + 4 k^{2} (- 7)}$

Step 3.3

Factor $4 k^{2}$ out of $4 k^{2} (k) + 4 k^{2} (- 7)$ .

$\frac{4 k^{2} (7 - k)}{k - 6} \cdot \frac{k - 4}{4 k^{2} (k - 7)}$

Step 4

Cancel the common factor of $4 k^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{4 k^{2} (7 - k)}{k - 6} \cdot \frac{k - 4}{4 k^{2} (k - 7)}$

Step 4.2

Rewrite the expression.

$\frac{7 - k}{k - 6} \cdot \frac{k - 4}{k - 7}$

Step 5

Multiply $\frac{7 - k}{k - 6}$ by $\frac{k - 4}{k - 7}$ .

$\frac{(7 - k) (k - 4)}{(k - 6) (k - 7)}$

Step 6

Cancel the common factor of $7 - k$ and $k - 7$ .

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Step 6.1

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{(- 1 (- 7) - k) (k - 4)}{(k - 6) (k - 7)}$

Step 6.2

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

$\frac{(- 1 (- 7) - (k)) (k - 4)}{(k - 6) (k - 7)}$

Step 6.3

Factor $- 1$ out of $- 1 (- 7) - (k)$ .

$\frac{- 1 (- 7 + k) (k - 4)}{(k - 6) (k - 7)}$

Step 6.4

Reorder terms.

$\frac{- 1 (k - 7) (k - 4)}{(k - 6) (k - 7)}$

Step 6.5

Cancel the common factor.

$\frac{- 1 (k - 7) (k - 4)}{(k - 6) (k - 7)}$

Step 6.6

Rewrite the expression.

$\frac{- 1 (k - 4)}{k - 6}$

Step 7

Move the negative in front of the fraction.

$- \frac{k - 4}{k - 6}$