Finite Math Examples

$\frac{t^{2} + 14 t + 48}{t^{2} - 25}$

Step 1

Factor $t^{2} + 14 t + 48$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $48$ and whose sum is $14$ .

$6, 8$

Step 1.2

Write the factored form using these integers.

$\frac{(t + 6) (t + 8)}{t^{2} - 25}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{(t + 6) (t + 8)}{t^{2} - 5^{2}}$

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 $a = t$ and $b = 5$ .

$\frac{(t + 6) (t + 8)}{(t + 5) (t - 5)}$