Simplify (x^2-36)/(x^2-11x+30)*(3x)/(x^3+6x^2)

$\frac{x^{2} - 36}{x^{2} - 11 x + 30} \cdot \frac{3 x}{x^{3} + 6 x^{2}}$

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 6^{2}}{x^{2} - 11 x + 30} \cdot \frac{3 x}{x^{3} + 6 x^{2}}$

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 $b = 6$ .

$\frac{(x + 6) (x - 6)}{x^{2} - 11 x + 30} \cdot \frac{3 x}{x^{3} + 6 x^{2}}$

Factor $x^{2} - 11 x + 30$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $30$ and whose sum is $- 11$ .

$- 6, - 5$

Write the factored form using these integers.

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

Simplify terms.

Factor $x^{2}$ out of $x^{3} + 6 x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

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

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

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

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 6$ .

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

Combine.

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

Cancel the common factor of $x + 6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $3 x$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Reorder factors in $\frac{3}{(x - 5) (x)}$ .

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

Simplify (x^2-36)/(x^2-11x+30)*(3x)/(x^3+6x^2)

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