Simplify (x^2+4x-5)/(15x^2+45x-60)*(10x^4+130x^3+360x^2)/(x+9)

$\frac{x^{2} + 4 x - 5}{15 x^{2} + 45 x - 60} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $x^{2} + 4 x - 5$ 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 $- 5$ and whose sum is $4$ .

$- 1, 5$

Write the factored form using these integers.

$\frac{(x - 1) (x + 5)}{15 x^{2} + 45 x - 60} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Simplify the denominator.

Factor $15$ out of $15 x^{2} + 45 x - 60$ .

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

$\frac{(x - 1) (x + 5)}{15 (x^{2}) + 45 x - 60} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $15$ out of $45 x$ .

$\frac{(x - 1) (x + 5)}{15 (x^{2}) + 15 (3 x) - 60} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $15$ out of $- 60$ .

$\frac{(x - 1) (x + 5)}{15 x^{2} + 15 (3 x) + 15 \cdot - 4} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $15$ out of $15 x^{2} + 15 (3 x)$ .

$\frac{(x - 1) (x + 5)}{15 (x^{2} + 3 x) + 15 \cdot - 4} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $15$ out of $15 (x^{2} + 3 x) + 15 \cdot - 4$ .

$\frac{(x - 1) (x + 5)}{15 (x^{2} + 3 x - 4)} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $x^{2} + 3 x - 4$ 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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

$\frac{(x - 1) (x + 5)}{15 ((x - 1) (x + 4))} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{4} + 130 x^{3} + 360 x^{2}}{x + 9}$

Simplify the numerator.

Factor $10 x^{2}$ out of $10 x^{4} + 130 x^{3} + 360 x^{2}$ .

Factor $10 x^{2}$ out of $10 x^{4}$ .

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x^{2}) + 130 x^{3} + 360 x^{2}}{x + 9}$

Factor $10 x^{2}$ out of $130 x^{3}$ .

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x^{2}) + 10 x^{2} (13 x) + 360 x^{2}}{x + 9}$

Factor $10 x^{2}$ out of $360 x^{2}$ .

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x^{2}) + 10 x^{2} (13 x) + 10 x^{2} (36)}{x + 9}$

Factor $10 x^{2}$ out of $10 x^{2} (x^{2}) + 10 x^{2} (13 x)$ .

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x^{2} + 13 x) + 10 x^{2} (36)}{x + 9}$

Factor $10 x^{2}$ out of $10 x^{2} (x^{2} + 13 x) + 10 x^{2} (36)$ .

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x^{2} + 13 x + 36)}{x + 9}$

Factor $x^{2} + 13 x + 36$ 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 $36$ and whose sum is $13$ .

$4, 9$

Write the factored form using these integers.

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} ((x + 4) (x + 9))}{x + 9}$

$\frac{(x - 1) (x + 5)}{15 (x - 1) (x + 4)} \cdot \frac{10 x^{2} (x + 4) (x + 9)}{x + 9}$

Simplify terms.

Cancel the common factor of $5 (x + 4)$ .

Factor $5 (x + 4)$ out of $15 (x - 1) (x + 4)$ .

$\frac{(x - 1) (x + 5)}{5 (x + 4) (3 (x - 1))} \cdot \frac{10 x^{2} (x + 4) (x + 9)}{x + 9}$

Factor $5 (x + 4)$ out of $10 x^{2} (x + 4) (x + 9)$ .

$\frac{(x - 1) (x + 5)}{5 (x + 4) (3 (x - 1))} \cdot \frac{5 (x + 4) (2 x^{2} (x + 9))}{x + 9}$

Cancel the common factor.

$\frac{(x - 1) (x + 5)}{5 (x + 4) (3 (x - 1))} \cdot \frac{5 (x + 4) (2 x^{2} (x + 9))}{x + 9}$

Rewrite the expression.

$\frac{(x - 1) (x + 5)}{3 (x - 1)} \cdot \frac{2 x^{2} (x + 9)}{x + 9}$

Multiply $\frac{(x - 1) (x + 5)}{3 (x - 1)}$ by $\frac{2 x^{2} (x + 9)}{x + 9}$ .

$\frac{(x - 1) (x + 5) (2 x^{2} (x + 9))}{3 (x - 1) (x + 9)}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x - 1) (x + 5) (2 x^{2} (x + 9))}{3 (x - 1) (x + 9)}$

Rewrite the expression.

$\frac{(x + 5) (2 x^{2} (x + 9))}{3 (x + 9)}$

Cancel the common factor of $x + 9$ .

Cancel the common factor.

$\frac{(x + 5) (2 x^{2} (x + 9))}{3 (x + 9)}$

Rewrite the expression.

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

Simplify the expression.

Move $2$ to the left of $x + 5$ .

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

Reorder factors in $\frac{2 (x + 5) x^{2}}{3}$ .

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

Simplify (x^2+4x-5)/(15x^2+45x-60)*(10x^4+130x^3+360x^2)/(x+9)

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