Basic Math Examples

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

Step 1

Factor $5 a$ out of $5 a^{2} + 25 a$ .

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Step 1.1

Factor $5 a$ out of $5 a^{2}$ .

$\frac{5 a (a) + 25 a}{a^{3} - 25 a}$

Step 1.2

Factor $5 a$ out of $25 a$ .

$\frac{5 a (a) + 5 a (5)}{a^{3} - 25 a}$

Step 1.3

Factor $5 a$ out of $5 a (a) + 5 a (5)$ .

$\frac{5 a (a + 5)}{a^{3} - 25 a}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $a$ out of $a^{3} - 25 a$ .

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Step 2.1.1

Factor $a$ out of $a^{3}$ .

$\frac{5 a (a + 5)}{a \cdot a^{2} - 25 a}$

Step 2.1.2

Factor $a$ out of $- 25 a$ .

$\frac{5 a (a + 5)}{a \cdot a^{2} + a \cdot - 25}$

Step 2.1.3

Factor $a$ out of $a \cdot a^{2} + a \cdot - 25$ .

$\frac{5 a (a + 5)}{a (a^{2} - 25)}$

Step 2.2

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

$\frac{5 a (a + 5)}{a (a^{2} - 5^{2})}$

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

$\frac{5 a (a + 5)}{a (a + 5) (a - 5)}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $a$ .

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Step 3.1.1

Cancel the common factor.

$\frac{5 a (a + 5)}{a (a + 5) (a - 5)}$

Step 3.1.2

Rewrite the expression.

$\frac{5 (a + 5)}{(a + 5) (a - 5)}$

Step 3.2

Cancel the common factor of $a + 5$ .

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Step 3.2.1

Cancel the common factor.

$\frac{5 (a + 5)}{(a + 5) (a - 5)}$

Step 3.2.2

Rewrite the expression.

$\frac{5}{a - 5}$