Trigonometry Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

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

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Factor $- 1$ out of $- x$ .

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

Step 2.1.3

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

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

Rewrite the expression.

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

Step 2.2

Move the negative in front of the fraction.

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