Basic Math Examples

$\frac{3 t - 15}{t^{2} - 25}$

Step 1

Factor $3$ out of $3 t - 15$ .

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Step 1.1

Factor $3$ out of $3 t$ .

$\frac{3 (t) - 15}{t^{2} - 25}$

Step 1.2

Factor $3$ out of $- 15$ .

$\frac{3 t + 3 \cdot - 5}{t^{2} - 25}$

Step 1.3

Factor $3$ out of $3 t + 3 \cdot - 5$ .

$\frac{3 (t - 5)}{t^{2} - 25}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{3 (t - 5)}{t^{2} - 5^{2}}$

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 $b = 5$ .

$\frac{3 (t - 5)}{(t + 5) (t - 5)}$

Step 3

Cancel the common factor of $t - 5$ .

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Step 3.1

Cancel the common factor.

$\frac{3 (t - 5)}{(t + 5) (t - 5)}$

Step 3.2

Rewrite the expression.

$\frac{3}{t + 5}$