Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

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

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

Step 3

Cancel the common factor of $5 + a$ and $a + 5$ .

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Step 3.1

Reorder terms.

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Divide $5 - a$ by $1$ .

$5 - a$