Basic Math Examples

$\frac{v - 5}{25 - v^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{v - 5}{5^{2} - v^{2}}$

Step 1.2

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 $b = v$ .

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $v - 5$ and $5 - v$ .

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Step 2.1.1

Factor $- 1$ out of $v$ .

$\frac{- 1 (- v) - 5}{(5 + v) (5 - v)}$

Step 2.1.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 (- v) - 1 (5)}{(5 + v) (5 - v)}$

Step 2.1.3

Factor $- 1$ out of $- 1 (- v) - 1 (5)$ .

$\frac{- 1 (- v + 5)}{(5 + v) (5 - v)}$

Step 2.1.4

Reorder terms.

$\frac{- 1 (- v + 5)}{(5 + v) (- v + 5)}$

Step 2.1.5

Cancel the common factor.

$\frac{- 1 (- v + 5)}{(5 + v) (- v + 5)}$

Step 2.1.6

Rewrite the expression.

$\frac{- 1}{5 + v}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{5 + v}$