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

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

Multiply the numerator and denominator of the complex fraction by $5 x^{2}$ .

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x^{2}$ .

Factor $x^{2}$ out of $5 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $5$ by $5$ .

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

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

Factor $5$ out of $5 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $5 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $1$ .

$\frac{25 + x^{2} \cdot - 1}{x^{3} + 5 x^{2} \cdot 1}$

Simplify the numerator.

Move $- 1$ to the left of $x^{2}$ .

$\frac{25 - 1 \cdot x^{2}}{x^{3} + 5 x^{2} \cdot 1}$

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$\frac{25 - x^{2}}{x^{3} + 5 x^{2} \cdot 1}$

Rewrite $25 - x^{2}$ in a factored form.

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

$\frac{5^{2} - x^{2}}{x^{3} + 5 x^{2} \cdot 1}$

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

$\frac{(5 + x) (5 - x)}{x^{3} + 5 x^{2} \cdot 1}$

Simplify the denominator.

Factor $x^{2}$ out of $x^{3} + 5 x^{2} \cdot 1$ .

Factor $x^{2}$ out of $x^{3}$ .

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

Factor $x^{2}$ out of $5 x^{2} \cdot 1$ .

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

Factor $x^{2}$ out of $x^{2} x + x^{2} (5 \cdot 1)$ .

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

Multiply $5$ by $1$ .

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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