Basic Math Examples

$\frac{g^{2} - 64}{49 g - 392} \div \frac{g - 8}{56}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{g^{2} - 64}{49 g - 392} \cdot \frac{56}{g - 8}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$\frac{g^{2} - 8^{2}}{49 g - 392} \cdot \frac{56}{g - 8}$

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 $a = g$ and $b = 8$ .

$\frac{(g + 8) (g - 8)}{49 g - 392} \cdot \frac{56}{g - 8}$

Step 3

Simplify terms.

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Step 3.1

Factor $49$ out of $49 g - 392$ .

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Step 3.1.1

Factor $49$ out of $49 g$ .

$\frac{(g + 8) (g - 8)}{49 (g) - 392} \cdot \frac{56}{g - 8}$

Step 3.1.2

Factor $49$ out of $- 392$ .

$\frac{(g + 8) (g - 8)}{49 g + 49 \cdot - 8} \cdot \frac{56}{g - 8}$

Step 3.1.3

Factor $49$ out of $49 g + 49 \cdot - 8$ .

$\frac{(g + 8) (g - 8)}{49 (g - 8)} \cdot \frac{56}{g - 8}$

Step 3.2

Cancel the common factor of $g - 8$ .

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Step 3.2.1

Factor $g - 8$ out of $(g + 8) (g - 8)$ .

$\frac{(g - 8) (g + 8)}{49 (g - 8)} \cdot \frac{56}{g - 8}$

Step 3.2.2

Cancel the common factor.

$\frac{(g - 8) (g + 8)}{49 (g - 8)} \cdot \frac{56}{g - 8}$

Step 3.2.3

Rewrite the expression.

$\frac{g + 8}{49 (g - 8)} \cdot 56$

Step 3.3

Cancel the common factor of $7$ .

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Step 3.3.1

Factor $7$ out of $49 (g - 8)$ .

$\frac{g + 8}{7 (7 (g - 8))} \cdot 56$

Step 3.3.2

Factor $7$ out of $56$ .

$\frac{g + 8}{7 (7 (g - 8))} \cdot (7 (8))$

Step 3.3.3

Cancel the common factor.

$\frac{g + 8}{7 (7 (g - 8))} \cdot (7 \cdot 8)$

Step 3.3.4

Rewrite the expression.

$\frac{g + 8}{7 (g - 8)} \cdot 8$

Step 3.4

Combine $\frac{g + 8}{7 (g - 8)}$ and $8$ .

$\frac{(g + 8) \cdot 8}{7 (g - 8)}$

Step 3.5

Move $8$ to the left of $g + 8$ .

$\frac{8 (g + 8)}{7 (g - 8)}$