Simplify (5+25/x)/(x/5-5/x)

$\frac{5 + \frac{25}{x}}{\frac{x}{5} - \frac{5}{x}}$

Multiply the numerator and denominator of the complex fraction by $x \cdot 5$ .

Multiply $\frac{5 + \frac{25}{x}}{\frac{x}{5} - \frac{5}{x}}$ by $\frac{x \cdot 5}{x \cdot 5}$ .

$\frac{x \cdot 5}{x \cdot 5} \cdot \frac{5 + \frac{25}{x}}{\frac{x}{5} - \frac{5}{x}}$

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x$ .

Factor $x$ out of $x \cdot 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $5$ by $25$ .

$\frac{x \cdot 5 \cdot 5 + 125}{x \cdot 5 \frac{x}{5} + x \cdot 5 (- \frac{5}{x})}$

Cancel the common factor of $5$ .

Factor $5$ out of $x \cdot 5$ .

$\frac{x \cdot 5 \cdot 5 + 125}{5 \cdot x \frac{x}{5} + x \cdot 5 (- \frac{5}{x})}$

Cancel the common factor.

$\frac{x \cdot 5 \cdot 5 + 125}{5 \cdot x \frac{x}{5} + x \cdot 5 (- \frac{5}{x})}$

Rewrite the expression.

$\frac{x \cdot 5 \cdot 5 + 125}{x \cdot x + x \cdot 5 (- \frac{5}{x})}$

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

$\frac{x \cdot 5 \cdot 5 + 125}{x^{1} x + x \cdot 5 (- \frac{5}{x})}$

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

$\frac{x \cdot 5 \cdot 5 + 125}{x^{1} x^{1} + x \cdot 5 (- \frac{5}{x})}$

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

$\frac{x \cdot 5 \cdot 5 + 125}{x^{1 + 1} + x \cdot 5 (- \frac{5}{x})}$

Add $1$ and $1$ .

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} + x \cdot 5 (- \frac{5}{x})}$

Cancel the common factor of $x$ .

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

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} + x \cdot 5 \frac{- 5}{x}}$

Factor $x$ out of $x \cdot 5$ .

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} + x (5) \frac{- 5}{x}}$

Cancel the common factor.

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} + x \cdot 5 \frac{- 5}{x}}$

Rewrite the expression.

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} + 5 \cdot - 5}$

Multiply $5$ by $- 5$ .

$\frac{x \cdot 5 \cdot 5 + 125}{x^{2} - 25}$

Simplify the numerator.

Move $5$ to the left of $x$ .

$\frac{5 \cdot x \cdot 5 + 125}{x^{2} - 25}$

Multiply $5$ by $5$ .

$\frac{25 x + 125}{x^{2} - 25}$

Factor $25$ out of $25 x + 125$ .

Factor $25$ out of $25 x$ .

$\frac{25 (x) + 125}{x^{2} - 25}$

Factor $25$ out of $125$ .

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

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

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

Simplify the denominator.

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

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

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 $b = 5$ .

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

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (5+25/x)/(x/5-5/x)

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