Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

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 $b = 5$ .

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

Factor $- 1$ out of $x$ .

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

Divide $(x + 5) \cdot (- 1)$ by $1$ .

$(x + 5) \cdot (- 1)$

Step 2.2

Simplify by multiplying through.

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Step 2.2.1

Apply the distributive property.

$x \cdot - 1 + 5 \cdot - 1$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $- 1$ to the left of $x$ .

$- 1 \cdot x + 5 \cdot - 1$

Step 2.2.2.2

Multiply $5$ by $- 1$ .

$- 1 \cdot x - 5$

Step 2.3

Rewrite $- 1 x$ as $- x$ .

$- x - 5$