Basic Math Examples

\frac{6 k^{3}}{k^{2} - 4} \div \frac{\frac{28 k^{7}}{- 6 k + 12}}{\frac{14 k + 28}{k}}

$\frac{6 k^{3}}{k^{2} - 4} \div \frac{\frac{28 k^{7}}{- 6 k + 12}}{\frac{14 k + 28}{k}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 k^{3}}{k^{2} - 4} \cdot \frac{\frac{14 k + 28}{k}}{\frac{28 k^{7}}{- 6 k + 12}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

$4$ as

$2^{2}$ .

$\frac{6 k^{3}}{k^{2} - 2^{2}} \cdot \frac{\frac{14 k + 28}{k}}{\frac{28 k^{7}}{- 6 k + 12}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = k$ and

$b = 2$ .

$\frac{6 k^{3}}{(k + 2) (k - 2)} \cdot \frac{\frac{14 k + 28}{k}}{\frac{28 k^{7}}{- 6 k + 12}}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{28 k^{7}}{- 6 k + 12}}$

Step 3.2

Cancel the common factor of

$28$ and

$- 6 k + 12$ .

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Step 3.2.1

Factor

$2$ out of

$28 k^{7}$ .

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{2 (14 k^{7})}{- 6 k + 12}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

$2$ out of

$- 6 k$ .

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{2 (14 k^{7})}{2 (- 3 k) + 12}}$

Step 3.2.2.2

Factor

$2$ out of

$12$ .

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{2 (14 k^{7})}{2 (- 3 k) + 2 (6)}}$

Step 3.2.2.3

Factor

$2$ out of

$2 (- 3 k) + 2 (6)$ .

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{2 (14 k^{7})}{2 (- 3 k + 6)}}$

Step 3.2.2.4

Cancel the common factor.

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{2 (14 k^{7})}{2 (- 3 k + 6)}}$

Step 3.2.2.5

Rewrite the expression.

$\frac{6 k^{3} \frac{14 k + 28}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{- 3 k + 6}}$

Step 3.3

Factor

$14$ out of

$14 k + 28$ .

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Step 3.3.1

Factor

$14$ out of

$14 k$ .

$\frac{6 k^{3} \frac{14 (k) + 28}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{- 3 k + 6}}$

Step 3.3.2

Factor

$14$ out of

$28$ .

$\frac{6 k^{3} \frac{14 k + 14 \cdot 2}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{- 3 k + 6}}$

Step 3.3.3

Factor

$14$ out of

$14 k + 14 \cdot 2$ .

$\frac{6 k^{3} \frac{14 (k + 2)}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{- 3 k + 6}}$

Step 3.4

Factor

$3$ out of

$- 3 k + 6$ .

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Step 3.4.1

Factor

$3$ out of

$- 3 k$ .

$\frac{6 k^{3} \frac{14 (k + 2)}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k) + 6}}$

Step 3.4.2

Factor

$3$ out of

$6$ .

$\frac{6 k^{3} \frac{14 (k + 2)}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k) + 3 (2)}}$

Step 3.4.3

Factor

$3$ out of

$3 (- k) + 3 (2)$ .

$\frac{6 k^{3} \frac{14 (k + 2)}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 4

Simplify the numerator.

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Step 4.1

Combine

$6$ and

$\frac{14 (k + 2)}{k}$ .

$\frac{k^{3} \frac{6 (14 (k + 2))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 4.2

Combine

$k^{3}$ and

$\frac{6 (14 (k + 2))}{k}$ .

$\frac{\frac{k^{3} (6 (14 (k + 2)))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 5

Multiply

$6$ by

$14$ .

$\frac{\frac{k^{3} (84 (k + 2))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite.

$\frac{\frac{k^{3} (6 (14 (k + 2)))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 6.2

Multiply

$6$ by

$14$ .

$\frac{\frac{k^{3} (84 (k + 2))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 6.3

Remove unnecessary parentheses.

$\frac{\frac{k^{3} \cdot 84 (k + 2)}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Reduce the expression

$\frac{k^{3} \cdot 84 (k + 2)}{k}$ by cancelling the common factors.

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Step 7.1.1

Factor

$k$ out of

$k^{3} \cdot 84 (k + 2)$ .

$\frac{\frac{k (k^{2} \cdot 84 (k + 2))}{k}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7.1.2

Raise

$k$ to the power of

$1$ .

$\frac{\frac{k (k^{2} \cdot 84 (k + 2))}{k^{1}}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7.1.3

Factor

$k$ out of

$k^{1}$ .

$\frac{\frac{k (k^{2} \cdot 84 (k + 2))}{k \cdot 1}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7.1.4

Cancel the common factor.

$\frac{\frac{k (k^{2} \cdot 84 (k + 2))}{k \cdot 1}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7.1.5

Rewrite the expression.

$\frac{\frac{k^{2} \cdot 84 (k + 2)}{1}}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 7.2

Divide

$k^{2} \cdot 84 (k + 2)$ by

$1$ .

$\frac{k^{2} \cdot 84 (k + 2)}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 8

Cancel the common factor of

$k + 2$ .

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Step 8.1

Cancel the common factor.

$\frac{k^{2} \cdot 84 (k + 2)}{(k + 2) (k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 8.2

Rewrite the expression.

$\frac{k^{2} \cdot 84}{(k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 9

Move

$84$ to the left of

$k^{2}$ .

$\frac{84 \cdot k^{2}}{(k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$

Step 10

Factor

$\frac{14 k^{7}}{3 (- k + 2)}$ out of

$\frac{84 \cdot k^{2}}{(k - 2) \frac{14 k^{7}}{3 (- k + 2)}}$ .

$\frac{3 (- k + 2)}{14 k^{7}} \cdot \frac{84 \cdot k^{2}}{k - 2}$

Step 11

Simplify terms.

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Step 11.1

Cancel the common factor of

$14 \cdot k^{2}$ .

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Step 11.1.1

Factor

$14 \cdot k^{2}$ out of

$14 k^{7}$ .

$\frac{3 (- k + 2)}{14 k^{2} (k^{5})} \cdot \frac{84 \cdot k^{2}}{k - 2}$

Step 11.1.2

Factor

$14 \cdot k^{2}$ out of

$84 \cdot k^{2}$ .

$\frac{3 (- k + 2)}{14 k^{2} (k^{5})} \cdot \frac{14 k^{2} (6)}{k - 2}$

Step 11.1.3

Cancel the common factor.

$\frac{3 (- k + 2)}{14 k^{2} k^{5}} \cdot \frac{14 k^{2} \cdot 6}{k - 2}$

Step 11.1.4

Rewrite the expression.

$\frac{3 (- k + 2)}{k^{5}} \cdot \frac{6}{k - 2}$

Step 11.2

Multiply

$\frac{3 (- k + 2)}{k^{5}}$ by

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

$\frac{3 (- k + 2) \cdot 6}{k^{5} (k - 2)}$

Step 11.3

Multiply

$6$ by

$3$ .

$\frac{18 (- k + 2)}{k^{5} (k - 2)}$

Step 11.4

Cancel the common factor of

$- k + 2$ and

$k - 2$ .

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Step 11.4.1

Factor

$- 1$ out of

$- k$ .

$\frac{18 (- (k) + 2)}{k^{5} (k - 2)}$

Step 11.4.2

Rewrite

$2$ as

$- 1 (- 2)$ .

$\frac{18 (- (k) - 1 (- 2))}{k^{5} (k - 2)}$

Step 11.4.3

Factor

$- 1$ out of

$- (k) - 1 (- 2)$ .

$\frac{18 (- (k - 2))}{k^{5} (k - 2)}$

Step 11.4.4

Rewrite

$- (k - 2)$ as

$- 1 (k - 2)$ .

$\frac{18 (- 1 (k - 2))}{k^{5} (k - 2)}$

Step 11.4.5

Cancel the common factor.

$\frac{18 (- 1 (k - 2))}{k^{5} (k - 2)}$

Step 11.4.6

Rewrite the expression.

$\frac{18 \cdot (- 1)}{k^{5}}$

Step 12

Multiply

$18$ by

$- 1$ .

$\frac{- 18}{k^{5}}$

Step 13

Move the negative in front of the fraction.

$- \frac{18}{k^{5}}$