Simplify (1-(x^2)/25)/(x/5+1)

$\frac{1 - \frac{x^{2}}{25}}{\frac{x}{5} + 1}$

Multiply the numerator and denominator of the complex fraction by $25$ .

Multiply $\frac{1 - \frac{x^{2}}{25}}{\frac{x}{5} + 1}$ by $\frac{25}{25}$ .

$\frac{25}{25} \cdot \frac{1 - \frac{x^{2}}{25}}{\frac{x}{5} + 1}$

Combine.

$\frac{25 (1 - \frac{x^{2}}{25})}{25 (\frac{x}{5} + 1)}$

Apply the distributive property.

$\frac{25 \cdot 1 + 25 (- \frac{x^{2}}{25})}{25 \frac{x}{5} + 25 \cdot 1}$

Simplify by cancelling.

Cancel the common factor of $25$ .

Move the leading negative in $- \frac{x^{2}}{25}$ into the numerator.

$\frac{25 \cdot 1 + 25 \frac{- x^{2}}{25}}{25 \frac{x}{5} + 25 \cdot 1}$

Cancel the common factor.

$\frac{25 \cdot 1 + 25 \frac{- x^{2}}{25}}{25 \frac{x}{5} + 25 \cdot 1}$

Rewrite the expression.

$\frac{25 \cdot 1 - x^{2}}{25 \frac{x}{5} + 25 \cdot 1}$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$\frac{25 \cdot 1 - x^{2}}{5 (5) \frac{x}{5} + 25 \cdot 1}$

Cancel the common factor.

$\frac{25 \cdot 1 - x^{2}}{5 \cdot 5 \frac{x}{5} + 25 \cdot 1}$

Rewrite the expression.

$\frac{25 \cdot 1 - x^{2}}{5 x + 25 \cdot 1}$

Simplify the numerator.

Rewrite $25 \cdot 1$ as ${(5 \cdot 1)}^{2}$ .

$\frac{{(5 \cdot 1)}^{2} - x^{2}}{5 x + 25 \cdot 1}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 \cdot 1$ and $b = x$ .

$\frac{(5 \cdot 1 + x) (5 \cdot 1 - x)}{5 x + 25 \cdot 1}$

Simplify.

Multiply $5$ by $1$ .

$\frac{(5 + x) (5 \cdot 1 - x)}{5 x + 25 \cdot 1}$

Multiply $5$ by $1$ .

$\frac{(5 + x) (5 - x)}{5 x + 25 \cdot 1}$

Simplify the denominator.

Factor $5$ out of $5 x + 25 \cdot 1$ .

Factor $5$ out of $5 x$ .

$\frac{(5 + x) (5 - x)}{5 (x) + 25 \cdot 1}$

Factor $5$ out of $25 \cdot 1$ .

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

Factor $5$ out of $5 (x) + 5 (5 \cdot 1)$ .

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

Multiply $5$ by $1$ .

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (1-(x^2)/25)/(x/5+1)

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