Precalculus Examples

$\frac{2 t - 6}{t^{2} - 9}$

Step 1

Factor $2$ out of $2 t - 6$ .

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Step 1.1

Factor $2$ out of $2 t$ .

$\frac{2 (t) - 6}{t^{2} - 9}$

Step 1.2

Factor $2$ out of $- 6$ .

$\frac{2 t + 2 \cdot - 3}{t^{2} - 9}$

Step 1.3

Factor $2$ out of $2 t + 2 \cdot - 3$ .

$\frac{2 (t - 3)}{t^{2} - 9}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{2 (t - 3)}{t^{2} - 3^{2}}$

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 $b = 3$ .

$\frac{2 (t - 3)}{(t + 3) (t - 3)}$

Step 3

Cancel the common factor of $t - 3$ .

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Step 3.1

Cancel the common factor.

$\frac{2 (t - 3)}{(t + 3) (t - 3)}$

Step 3.2

Rewrite the expression.

$\frac{2}{t + 3}$