Trigonometry Examples

$\frac{5 t - 10}{t^{2} - 4}$

Step 1

Factor $5$ out of $5 t - 10$ .

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Step 1.1

Factor $5$ out of $5 t$ .

$\frac{5 (t) - 10}{t^{2} - 4}$

Step 1.2

Factor $5$ out of $- 10$ .

$\frac{5 t + 5 \cdot - 2}{t^{2} - 4}$

Step 1.3

Factor $5$ out of $5 t + 5 \cdot - 2$ .

$\frac{5 (t - 2)}{t^{2} - 4}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Step 3

Cancel the common factor of $t - 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{5}{t + 2}$