Simplify (3/x-3)/(5-25/x)

$\frac{\frac{3}{x} - 3}{5 - \frac{25}{x}}$

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

Multiply $\frac{\frac{3}{x} - 3}{5 - \frac{25}{x}}$ by $\frac{x}{x}$ .

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

Combine.

$\frac{x (\frac{3}{x} - 3)}{x (5 - \frac{25}{x})}$

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Factor $3$ out of $3 + x \cdot - 3$ .

Factor $3$ out of $3$ .

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

Factor $3$ out of $x \cdot - 3$ .

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

Factor $3$ out of $3 (1) + 3 (x \cdot - 1)$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

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

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

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

Factor $5$ out of $- 25$ .

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

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

$\frac{3 (1 - x)}{5 (x - 5)}$