Simplify (x^4-4x^2)/(5x^5+45x^4+70x^3)*(5x+35)/(x+10)

$\frac{x^{4} - 4 x^{2}}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Simplify the numerator.

Factor $x^{2}$ out of $x^{4} - 4 x^{2}$ .

Factor $x^{2}$ out of $x^{4}$ .

$\frac{x^{2} x^{2} - 4 x^{2}}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Factor $x^{2}$ out of $- 4 x^{2}$ .

$\frac{x^{2} x^{2} + x^{2} \cdot - 4}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} \cdot - 4$ .

$\frac{x^{2} (x^{2} - 4)}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Rewrite $4$ as $2^{2}$ .

$\frac{x^{2} (x^{2} - 2^{2})}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

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 $b = 2$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{5} + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Simplify the denominator.

Factor $5 x^{3}$ out of $5 x^{5} + 45 x^{4} + 70 x^{3}$ .

Factor $5 x^{3}$ out of $5 x^{5}$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x^{2}) + 45 x^{4} + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Factor $5 x^{3}$ out of $45 x^{4}$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x^{2}) + 5 x^{3} (9 x) + 70 x^{3}} \cdot \frac{5 x + 35}{x + 10}$

Factor $5 x^{3}$ out of $70 x^{3}$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x^{2}) + 5 x^{3} (9 x) + 5 x^{3} (14)} \cdot \frac{5 x + 35}{x + 10}$

Factor $5 x^{3}$ out of $5 x^{3} (x^{2}) + 5 x^{3} (9 x)$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x^{2} + 9 x) + 5 x^{3} (14)} \cdot \frac{5 x + 35}{x + 10}$

Factor $5 x^{3}$ out of $5 x^{3} (x^{2} + 9 x) + 5 x^{3} (14)$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x^{2} + 9 x + 14)} \cdot \frac{5 x + 35}{x + 10}$

Factor $x^{2} + 9 x + 14$ 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 $14$ and whose sum is $9$ .

$2, 7$

Write the factored form using these integers.

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} ((x + 2) (x + 7))} \cdot \frac{5 x + 35}{x + 10}$

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x + 2) (x + 7)} \cdot \frac{5 x + 35}{x + 10}$

Simplify terms.

Factor $5$ out of $5 x + 35$ .

Factor $5$ out of $5 x$ .

$\frac{x^{2} (x + 2) (x - 2)}{5 x^{3} (x + 2) (x + 7)} \cdot \frac{5 (x) + 35}{x + 10}$

Factor $5$ out of $35$ .

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

Factor $5$ out of $5 x + 5 \cdot 7$ .

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

Cancel the common factor of $5 (x + 7)$ .

Factor $5 (x + 7)$ out of $5 x^{3} (x + 2) (x + 7)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{2} (x + 2) (x - 2)}{x^{3} (x + 2)} \cdot \frac{1}{x + 10}$

Multiply $\frac{x^{2} (x + 2) (x - 2)}{x^{3} (x + 2)}$ by $\frac{1}{x + 10}$ .

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

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{(x + 2) (x - 2)}{(x (x + 2)) (x + 10)}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x + 2) (x - 2)}{x (x + 2) (x + 10)}$

Rewrite the expression.

$\frac{x - 2}{(x) (x + 10)}$

$\frac{x - 2}{x (x + 10)}$

Simplify (x^4-4x^2)/(5x^5+45x^4+70x^3)*(5x+35)/(x+10)

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