Simplify (x^2-10x)/(15x^3-60x^2-900x)*(x^2+14x+48)/(x+8)

$\frac{x^{2} - 10 x}{15 x^{3} - 60 x^{2} - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $x$ out of $x^{2} - 10 x$ .

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

$\frac{x \cdot x - 10 x}{15 x^{3} - 60 x^{2} - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $x$ out of $- 10 x$ .

$\frac{x \cdot x + x \cdot - 10}{15 x^{3} - 60 x^{2} - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $x$ out of $x \cdot x + x \cdot - 10$ .

$\frac{x (x - 10)}{15 x^{3} - 60 x^{2} - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Simplify the denominator.

Factor $15 x$ out of $15 x^{3} - 60 x^{2} - 900 x$ .

Factor $15 x$ out of $15 x^{3}$ .

$\frac{x (x - 10)}{15 x (x^{2}) - 60 x^{2} - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $15 x$ out of $- 60 x^{2}$ .

$\frac{x (x - 10)}{15 x (x^{2}) + 15 x (- 4 x) - 900 x} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $15 x$ out of $- 900 x$ .

$\frac{x (x - 10)}{15 x (x^{2}) + 15 x (- 4 x) + 15 x (- 60)} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $15 x$ out of $15 x (x^{2}) + 15 x (- 4 x)$ .

$\frac{x (x - 10)}{15 x (x^{2} - 4 x) + 15 x (- 60)} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $15 x$ out of $15 x (x^{2} - 4 x) + 15 x (- 60)$ .

$\frac{x (x - 10)}{15 x (x^{2} - 4 x - 60)} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $x^{2} - 4 x - 60$ 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 $- 60$ and whose sum is $- 4$ .

$- 10, 6$

Write the factored form using these integers.

$\frac{x (x - 10)}{15 x ((x - 10) (x + 6))} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

$\frac{x (x - 10)}{15 x (x - 10) (x + 6)} \cdot \frac{x^{2} + 14 x + 48}{x + 8}$

Factor $x^{2} + 14 x + 48$ 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 $48$ and whose sum is $14$ .

$6, 8$

Write the factored form using these integers.

$\frac{x (x - 10)}{15 x (x - 10) (x + 6)} \cdot \frac{(x + 6) (x + 8)}{x + 8}$

Simplify terms.

Cancel the common factor of $x + 6$ .

Factor $x + 6$ out of $15 x (x - 10) (x + 6)$ .

$\frac{x (x - 10)}{(x + 6) (15 x (x - 10))} \cdot \frac{(x + 6) (x + 8)}{x + 8}$

Cancel the common factor.

$\frac{x (x - 10)}{(x + 6) (15 x (x - 10))} \cdot \frac{(x + 6) (x + 8)}{x + 8}$

Rewrite the expression.

$\frac{x (x - 10)}{15 x (x - 10)} \cdot \frac{x + 8}{x + 8}$

Multiply $\frac{x (x - 10)}{15 x (x - 10)}$ by $\frac{x + 8}{x + 8}$ .

$\frac{x (x - 10) (x + 8)}{15 x (x - 10) (x + 8)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (x - 10) (x + 8)}{15 x (x - 10) (x + 8)}$

Rewrite the expression.

$\frac{(x - 10) (x + 8)}{(15 (x - 10)) (x + 8)}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{(x - 10) (x + 8)}{15 (x - 10) (x + 8)}$

Rewrite the expression.

$\frac{x + 8}{(15) (x + 8)}$

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{x + 8}{15 (x + 8)}$

Rewrite the expression.

$\frac{1}{15}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$

Simplify (x^2-10x)/(15x^3-60x^2-900x)*(x^2+14x+48)/(x+8)

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