Simplify (x^2-7x)/(10x^3)*(5x+15)/(x^2-4x-21)

$\frac{x^{2} - 7 x}{10 x^{3}} \cdot \frac{5 x + 15}{x^{2} - 4 x - 21}$

Simplify with factoring out.

Factor $x$ out of $x^{2} - 7 x$ .

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

$\frac{x \cdot x - 7 x}{10 x^{3}} \cdot \frac{5 x + 15}{x^{2} - 4 x - 21}$

Factor $x$ out of $- 7 x$ .

$\frac{x \cdot x + x \cdot - 7}{10 x^{3}} \cdot \frac{5 x + 15}{x^{2} - 4 x - 21}$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$\frac{x (x - 7)}{10 x^{3}} \cdot \frac{5 x + 15}{x^{2} - 4 x - 21}$

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

Factor $5$ out of $5 x$ .

$\frac{x (x - 7)}{10 x^{3}} \cdot \frac{5 (x) + 15}{x^{2} - 4 x - 21}$

Factor $5$ out of $15$ .

$\frac{x (x - 7)}{10 x^{3}} \cdot \frac{5 x + 5 \cdot 3}{x^{2} - 4 x - 21}$

Factor $5$ out of $5 x + 5 \cdot 3$ .

$\frac{x (x - 7)}{10 x^{3}} \cdot \frac{5 (x + 3)}{x^{2} - 4 x - 21}$

Factor $x^{2} - 4 x - 21$ 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 $- 21$ and whose sum is $- 4$ .

$- 7, 3$

Write the factored form using these integers.

$\frac{x (x - 7)}{10 x^{3}} \cdot \frac{5 (x + 3)}{(x - 7) (x + 3)}$

Simplify terms.

Combine.

$\frac{x (x - 7) (5 (x + 3))}{10 x^{3} ((x - 7) (x + 3))}$

Cancel the common factor of $x$ and $x^{3}$ .

Factor $x$ out of $x (x - 7) (5 (x + 3))$ .

$\frac{x ((x - 7) (5 (x + 3)))}{10 x^{3} ((x - 7) (x + 3))}$

Cancel the common factors.

Factor $x$ out of $10 x^{3} ((x - 7) (x + 3))$ .

$\frac{x ((x - 7) (5 (x + 3)))}{x (10 x^{2} ((x - 7) (x + 3)))}$

Cancel the common factor.

$\frac{x ((x - 7) (5 (x + 3)))}{x (10 x^{2} ((x - 7) (x + 3)))}$

Rewrite the expression.

$\frac{(x - 7) (5 (x + 3))}{10 x^{2} ((x - 7) (x + 3))}$

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{(x - 7) (5 (x + 3))}{10 x^{2} ((x - 7) (x + 3))}$

Rewrite the expression.

$\frac{5 (x + 3)}{10 x^{2} (x + 3)}$

Cancel the common factors.

Factor $5$ out of $10 x^{2} (x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 x^{2}}$

Simplify (x^2-7x)/(10x^3)*(5x+15)/(x^2-4x-21)

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