Basic Math Examples

$\frac{20 r}{r^{2} - 49} \div \frac{4 r - 16}{7 r + 49}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{20 r}{r^{2} - 49} \cdot \frac{7 r + 49}{4 r - 16}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{20 r}{r^{2} - 7^{2}} \cdot \frac{7 r + 49}{4 r - 16}$

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 $a = r$ and $b = 7$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 r + 49}{4 r - 16}$

Step 3

Simplify terms.

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Step 3.1

Factor $7$ out of $7 r + 49$ .

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Step 3.1.1

Factor $7$ out of $7 r$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 (r) + 49}{4 r - 16}$

Step 3.1.2

Factor $7$ out of $49$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 r + 7 \cdot 7}{4 r - 16}$

Step 3.1.3

Factor $7$ out of $7 r + 7 \cdot 7$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 r - 16}$

Step 3.2

Factor $4$ out of $4 r - 16$ .

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Step 3.2.1

Factor $4$ out of $4 r$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 (r) - 16}$

Step 3.2.2

Factor $4$ out of $- 16$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 r + 4 \cdot - 4}$

Step 3.2.3

Factor $4$ out of $4 r + 4 \cdot - 4$ .

$\frac{20 r}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 (r - 4)}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $20 r$ .

$\frac{4 (5 r)}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 (r - 4)}$

Step 3.3.2

Cancel the common factor.

$\frac{4 (5 r)}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{4 (r - 4)}$

Step 3.3.3

Rewrite the expression.

$\frac{5 r}{(r + 7) (r - 7)} \cdot \frac{7 (r + 7)}{r - 4}$

Step 3.4

Cancel the common factor of $r + 7$ .

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Step 3.4.1

Factor $r + 7$ out of $7 (r + 7)$ .

$\frac{5 r}{(r + 7) (r - 7)} \cdot \frac{(r + 7) \cdot 7}{r - 4}$

Step 3.4.2

Cancel the common factor.

$\frac{5 r}{(r + 7) (r - 7)} \cdot \frac{(r + 7) \cdot 7}{r - 4}$

Step 3.4.3

Rewrite the expression.

$\frac{5 r}{r - 7} \cdot \frac{7}{r - 4}$

Step 3.5

Multiply $\frac{5 r}{r - 7}$ by $\frac{7}{r - 4}$ .

$\frac{5 r \cdot 7}{(r - 7) (r - 4)}$

Step 3.6

Multiply $7$ by $5$ .

$\frac{35 r}{(r - 7) (r - 4)}$