Basic Math Examples

$\frac{\frac{4 t + 9}{t + 6}}{16 t^{2} - 81}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 t + 9}{t + 6} \cdot \frac{1}{16 t^{2} - 81}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16 t^{2}$ as ${(4 t)}^{2}$ .

$\frac{4 t + 9}{t + 6} \cdot \frac{1}{{(4 t)}^{2} - 81}$

Step 2.2

Rewrite $81$ as $9^{2}$ .

$\frac{4 t + 9}{t + 6} \cdot \frac{1}{{(4 t)}^{2} - 9^{2}}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 t$ and $b = 9$ .

$\frac{4 t + 9}{t + 6} \cdot \frac{1}{(4 t + 9) (4 t - 9)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $4 t + 9$ .

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Step 3.1.1

Cancel the common factor.

$\frac{4 t + 9}{t + 6} \cdot \frac{1}{(4 t + 9) (4 t - 9)}$

Step 3.1.2

Rewrite the expression.

$\frac{1}{t + 6} \cdot \frac{1}{4 t - 9}$

Step 3.2

Multiply $\frac{1}{t + 6}$ by $\frac{1}{4 t - 9}$ .

$\frac{1}{(t + 6) (4 t - 9)}$