Simplify (15x+15)/(5x^3-50x^2)*(x^2-100)/(x^2+2x-80)

$\frac{15 x + 15}{5 x^{3} - 50 x^{2}} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Simplify with factoring out.

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

Factor $15$ out of $15 x$ .

$\frac{15 (x) + 15}{5 x^{3} - 50 x^{2}} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Factor $15$ out of $15$ .

$\frac{15 (x) + 15 (1)}{5 x^{3} - 50 x^{2}} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Factor $15$ out of $15 (x) + 15 (1)$ .

$\frac{15 (x + 1)}{5 x^{3} - 50 x^{2}} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Factor $5 x^{2}$ out of $5 x^{3} - 50 x^{2}$ .

Factor $5 x^{2}$ out of $5 x^{3}$ .

$\frac{15 (x + 1)}{5 x^{2} (x) - 50 x^{2}} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Factor $5 x^{2}$ out of $- 50 x^{2}$ .

$\frac{15 (x + 1)}{5 x^{2} (x) + 5 x^{2} (- 10)} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

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

$\frac{15 (x + 1)}{5 x^{2} (x - 10)} \cdot \frac{x^{2} - 100}{x^{2} + 2 x - 80}$

Simplify the numerator.

Rewrite $100$ as $10^{2}$ .

$\frac{15 (x + 1)}{5 x^{2} (x - 10)} \cdot \frac{x^{2} - 10^{2}}{x^{2} + 2 x - 80}$

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 $b = 10$ .

$\frac{15 (x + 1)}{5 x^{2} (x - 10)} \cdot \frac{(x + 10) (x - 10)}{x^{2} + 2 x - 80}$

Factor $x^{2} + 2 x - 80$ 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 $- 80$ and whose sum is $2$ .

$- 8, 10$

Write the factored form using these integers.

$\frac{15 (x + 1)}{5 x^{2} (x - 10)} \cdot \frac{(x + 10) (x - 10)}{(x - 8) (x + 10)}$

Simplify terms.

Combine.

$\frac{15 (x + 1) ((x + 10) (x - 10))}{5 x^{2} (x - 10) ((x - 8) (x + 10))}$

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 (x + 1) ((x + 10) (x - 10))$ .

$\frac{5 (3 (x + 1) ((x + 10) (x - 10)))}{5 x^{2} (x - 10) ((x - 8) (x + 10))}$

Cancel the common factors.

Factor $5$ out of $5 x^{2} (x - 10) ((x - 8) (x + 10))$ .

$\frac{5 (3 (x + 1) ((x + 10) (x - 10)))}{5 ((x^{2} (x - 10)) ((x - 8) (x + 10)))}$

Cancel the common factor.

$\frac{5 (3 (x + 1) ((x + 10) (x - 10)))}{5 ((x^{2} (x - 10)) ((x - 8) (x + 10)))}$

Rewrite the expression.

$\frac{3 (x + 1) ((x + 10) (x - 10))}{(x^{2} (x - 10)) ((x - 8) (x + 10))}$

Cancel the common factor of $x + 10$ .

Cancel the common factor.

$\frac{3 (x + 1) ((x + 10) (x - 10))}{x^{2} (x - 10) ((x - 8) (x + 10))}$

Rewrite the expression.

$\frac{3 (x + 1) (x - 10)}{(x^{2} (x - 10)) (x - 8)}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{3 (x + 1) (x - 10)}{x^{2} (x - 10) (x - 8)}$

Rewrite the expression.

$\frac{3 (x + 1)}{(x^{2}) (x - 8)}$

$\frac{3 (x + 1)}{x^{2} (x - 8)}$

Simplify (15x+15)/(5x^3-50x^2)*(x^2-100)/(x^2+2x-80)

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