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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $5$ .

Factor $5$ out of $25 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Cancel the common factor of $25$ .

Factor $25$ out of $25 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5 x$ .

Factor $5 x$ out of $25 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Factor $5 x$ out of $5 x^{3} + 25 x \cdot - 5$ .

Factor $5 x$ out of $5 x^{3}$ .

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

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

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

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

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

Multiply $5$ by $- 5$ .

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

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

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

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 $b = 5$ .

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

Simplify terms.

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Divide $5 x (x - 5)$ by $1$ .

$5 x (x - 5)$

Apply the distributive property.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 5$ by $5$ .

$5 x^{2} - 25 x$

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

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