Pre-Algebra Examples

$\frac{16 x^{2} - 25}{5 - 4 x}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\frac{{(4 x)}^{2} - 25}{5 - 4 x}$

Step 1.2

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

$\frac{{(4 x)}^{2} - 5^{2}}{5 - 4 x}$

Step 1.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x$ and $b = 5$ .

$\frac{(4 x + 5) (4 x - 5)}{5 - 4 x}$

Step 2

Cancel the common factor of $4 x - 5$ and $5 - 4 x$ .

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Step 2.1

Factor $- 1$ out of $4 x$ .

$\frac{(4 x + 5) (- (- 4 x) - 5)}{5 - 4 x}$

Step 2.2

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

$\frac{(4 x + 5) (- (- 4 x) - 1 (5))}{5 - 4 x}$

Step 2.3

Factor $- 1$ out of $- (- 4 x) - 1 (5)$ .

$\frac{(4 x + 5) (- (- 4 x + 5))}{5 - 4 x}$

Step 2.4

Rewrite $- (- 4 x + 5)$ as $- 1 (- 4 x + 5)$ .

$\frac{(4 x + 5) (- 1 (- 4 x + 5))}{5 - 4 x}$

Step 2.5

Reorder terms.

$\frac{(4 x + 5) (- 1 (- 4 x + 5))}{- 4 x + 5}$

Step 2.6

Cancel the common factor.

$\frac{(4 x + 5) (- 1 (- 4 x + 5))}{- 4 x + 5}$

Step 2.7

Divide $(4 x + 5) \cdot (- 1)$ by $1$ .

$(4 x + 5) \cdot (- 1)$

Step 3

Apply the distributive property.

$4 x \cdot - 1 + 5 \cdot - 1$

Step 4

Multiply $- 1$ by $4$ .

$- 4 x + 5 \cdot - 1$

Step 5

Multiply $5$ by $- 1$ .

$- 4 x - 5$