Simplify (x^2-25)/(3-x)*(x-3)/(x+5)

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

Simplify the numerator.

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

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

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 $b = 5$ .

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

Simplify terms.

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify terms.

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

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

Cancel the common factor of $x - 3$ and $3 - x$ .

Factor $- 1$ out of $x$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

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

Factor $- 1$ out of $- 1 (- x) - 1 (3)$ .

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

Reorder terms.

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

Cancel the common factor.

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

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

$(x - 5) \cdot (- 1)$

Apply the distributive property.

$x \cdot - 1 - 5 \cdot - 1$

Simplify the expression.

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

$- 1 \cdot x - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$- 1 \cdot x + 5$

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

$- x + 5$