Basic Math Examples

$\frac{7 s + 8}{s + 3} \div (49 s^{2} - 64)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{7 s + 8}{s + 3}}{49 s^{2} - 64}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 s + 8}{s + 3} \cdot \frac{1}{49 s^{2} - 64}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $49 s^{2}$ as ${(7 s)}^{2}$ .

$\frac{7 s + 8}{s + 3} \cdot \frac{1}{{(7 s)}^{2} - 64}$

Step 3.2

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

$\frac{7 s + 8}{s + 3} \cdot \frac{1}{{(7 s)}^{2} - 8^{2}}$

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 s$ and $b = 8$ .

$\frac{7 s + 8}{s + 3} \cdot \frac{1}{(7 s + 8) (7 s - 8)}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $7 s + 8$ .

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Step 4.1.1

Cancel the common factor.

$\frac{7 s + 8}{s + 3} \cdot \frac{1}{(7 s + 8) (7 s - 8)}$

Step 4.1.2

Rewrite the expression.

$\frac{1}{s + 3} \cdot \frac{1}{7 s - 8}$

Step 4.2

Multiply $\frac{1}{s + 3}$ by $\frac{1}{7 s - 8}$ .

$\frac{1}{(s + 3) (7 s - 8)}$