Simplify (5x^2-45)/(15-5x)*(2x^2-6x)/(x+3)

$\frac{5 x^{2} - 45}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Step 1

Simplify the numerator.

Factor $5$ out of $5 x^{2} - 45$ .

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

$\frac{5 (x^{2}) - 45}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Factor $5$ out of $- 45$ .

$\frac{5 x^{2} + 5 \cdot - 9}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Factor $5$ out of $5 x^{2} + 5 \cdot - 9$ .

$\frac{5 (x^{2} - 9)}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Rewrite $9$ as $3^{2}$ .

$\frac{5 (x^{2} - 3^{2})}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

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 $b = 3$ .

$\frac{5 (x + 3) (x - 3)}{15 - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Step 2

Simplify terms.

Factor $5$ out of $15 - 5 x$ .

Factor $5$ out of $15$ .

$\frac{5 (x + 3) (x - 3)}{5 (3) - 5 x} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Factor $5$ out of $- 5 x$ .

$\frac{5 (x + 3) (x - 3)}{5 (3) + 5 (- x)} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Factor $5$ out of $5 (3) + 5 (- x)$ .

$\frac{5 (x + 3) (x - 3)}{5 (3 - x)} \cdot \frac{2 x^{2} - 6 x}{x + 3}$

Factor $2 x$ out of $2 x^{2} - 6 x$ .

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

$\frac{5 (x + 3) (x - 3)}{5 (3 - x)} \cdot \frac{2 x (x) - 6 x}{x + 3}$

Factor $2 x$ out of $- 6 x$ .

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

Factor $2 x$ out of $2 x (x) + 2 x (- 3)$ .

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

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of $5 (x + 3) (x - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $2$ and $\frac{5 (x - 3)}{5 (3 - x)}$ .

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

Multiply $5$ by $2$ .

$\frac{10 (x - 3)}{5 (3 - x)} \cdot (x (x - 3))$

Combine $x$ and $\frac{10 (x - 3)}{5 (3 - x)}$ .

$\frac{x (10 (x - 3))}{5 (3 - x)} \cdot (x - 3)$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $x \cdot 10 (x - 3)$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{x \cdot 2 (x - 3)}{3 - x} \cdot (x - 3)$

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

Factor $- 1$ out of $x$ .

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Divide $x \cdot 2 \cdot (- 1)$ by $1$ .

$x \cdot 2 \cdot (- 1) \cdot (x - 3)$

Simplify the expression.

Move $2$ to the left of $x$ .

$2 \cdot x \cdot - 1 \cdot (x - 3)$

Multiply $- 1$ by $2$ .

$- 2 x \cdot (x - 3)$

Apply the distributive property.

$- 2 x \cdot x - 2 x \cdot - 3$

Step 3

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

Move $x$ .

$- 2 (x \cdot x) - 2 x \cdot - 3$

Multiply $x$ by $x$ .

$- 2 x^{2} - 2 x \cdot - 3$

Step 4

Multiply $- 3$ by $- 2$ .

$- 2 x^{2} + 6 x$

Simplify (5x^2-45)/(15-5x)*(2x^2-6x)/(x+3)

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