Simplify (9x-45)/(3x^5+24x^4+36x^3)*(x^3-8x^2-20x)/(x^2-15x+50)

$\frac{9 x - 45}{3 x^{5} + 24 x^{4} + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $9$ out of $9 x - 45$ .

Factor $9$ out of $9 x$ .

$\frac{9 (x) - 45}{3 x^{5} + 24 x^{4} + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $9$ out of $- 45$ .

$\frac{9 x + 9 \cdot - 5}{3 x^{5} + 24 x^{4} + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $9$ out of $9 x + 9 \cdot - 5$ .

$\frac{9 (x - 5)}{3 x^{5} + 24 x^{4} + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Simplify the denominator.

Factor $3 x^{3}$ out of $3 x^{5} + 24 x^{4} + 36 x^{3}$ .

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

$\frac{9 (x - 5)}{3 x^{3} (x^{2}) + 24 x^{4} + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $3 x^{3}$ out of $24 x^{4}$ .

$\frac{9 (x - 5)}{3 x^{3} (x^{2}) + 3 x^{3} (8 x) + 36 x^{3}} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $3 x^{3}$ out of $36 x^{3}$ .

$\frac{9 (x - 5)}{3 x^{3} (x^{2}) + 3 x^{3} (8 x) + 3 x^{3} (12)} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $3 x^{3}$ out of $3 x^{3} (x^{2}) + 3 x^{3} (8 x)$ .

$\frac{9 (x - 5)}{3 x^{3} (x^{2} + 8 x) + 3 x^{3} (12)} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $3 x^{3}$ out of $3 x^{3} (x^{2} + 8 x) + 3 x^{3} (12)$ .

$\frac{9 (x - 5)}{3 x^{3} (x^{2} + 8 x + 12)} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $x^{2} + 8 x + 12$ 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 $12$ and whose sum is $8$ .

$2, 6$

Write the factored form using these integers.

$\frac{9 (x - 5)}{3 x^{3} ((x + 2) (x + 6))} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x^{3} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Simplify the numerator.

Factor $x$ out of $x^{3} - 8 x^{2} - 20 x$ .

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

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x \cdot x^{2} - 8 x^{2} - 20 x}{x^{2} - 15 x + 50}$

Factor $x$ out of $- 8 x^{2}$ .

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x \cdot x^{2} + x (- 8 x) - 20 x}{x^{2} - 15 x + 50}$

Factor $x$ out of $- 20 x$ .

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x \cdot x^{2} + x (- 8 x) + x \cdot - 20}{x^{2} - 15 x + 50}$

Factor $x$ out of $x \cdot x^{2} + x (- 8 x)$ .

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x (x^{2} - 8 x) + x \cdot - 20}{x^{2} - 15 x + 50}$

Factor $x$ out of $x (x^{2} - 8 x) + x \cdot - 20$ .

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x (x^{2} - 8 x - 20)}{x^{2} - 15 x + 50}$

Factor $x^{2} - 8 x - 20$ 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 $- 20$ and whose sum is $- 8$ .

$- 10, 2$

Write the factored form using these integers.

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x ((x - 10) (x + 2))}{x^{2} - 15 x + 50}$

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x (x - 10) (x + 2)}{x^{2} - 15 x + 50}$

Factor $x^{2} - 15 x + 50$ 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 $50$ and whose sum is $- 15$ .

$- 10, - 5$

Write the factored form using these integers.

$\frac{9 (x - 5)}{3 x^{3} (x + 2) (x + 6)} \cdot \frac{x (x - 10) (x + 2)}{(x - 10) (x - 5)}$

Simplify terms.

Combine.

$\frac{9 (x - 5) (x (x - 10) (x + 2))}{3 x^{3} (x + 2) (x + 6) ((x - 10) (x - 5))}$

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 (x - 5) (x (x - 10) (x + 2))$ .

$\frac{3 (3 (x - 5) (x (x - 10) (x + 2)))}{3 x^{3} (x + 2) (x + 6) ((x - 10) (x - 5))}$

Cancel the common factors.

Factor $3$ out of $3 x^{3} (x + 2) (x + 6) ((x - 10) (x - 5))$ .

$\frac{3 (3 (x - 5) (x (x - 10) (x + 2)))}{3 (((x^{3} (x + 2)) (x + 6)) ((x - 10) (x - 5)))}$

Cancel the common factor.

$\frac{3 (3 (x - 5) (x (x - 10) (x + 2)))}{3 (((x^{3} (x + 2)) (x + 6)) ((x - 10) (x - 5)))}$

Rewrite the expression.

$\frac{3 (x - 5) (x (x - 10) (x + 2))}{((x^{3} (x + 2)) (x + 6)) ((x - 10) (x - 5))}$

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{3 (x - 5) (x (x - 10) (x + 2))}{(x^{3} (x + 2)) (x + 6) ((x - 10) (x - 5))}$

Rewrite the expression.

$\frac{3 (x (x - 10) (x + 2))}{((x^{3} (x + 2)) (x + 6)) (x - 10)}$

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

Factor $x$ out of $3 (x (x - 10) (x + 2))$ .

$\frac{x (3 ((x - 10) (x + 2)))}{((x^{3} (x + 2)) (x + 6)) (x - 10)}$

Cancel the common factors.

Factor $x$ out of $((x^{3} (x + 2)) (x + 6)) (x - 10)$ .

$\frac{x (3 ((x - 10) (x + 2)))}{x (((x^{2} (x + 2)) (x + 6)) (x - 10))}$

Cancel the common factor.

$\frac{x (3 ((x - 10) (x + 2)))}{x (((x^{2} (x + 2)) (x + 6)) (x - 10))}$

Rewrite the expression.

$\frac{3 ((x - 10) (x + 2))}{((x^{2} (x + 2)) (x + 6)) (x - 10)}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{3 ((x - 10) (x + 2))}{(x^{2} (x + 2)) (x + 6) (x - 10)}$

Rewrite the expression.

$\frac{3 (x + 2)}{(x^{2} (x + 2)) (x + 6)}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{3 (x + 2)}{x^{2} (x + 2) (x + 6)}$

Rewrite the expression.

$\frac{3}{(x^{2}) (x + 6)}$

$\frac{3}{x^{2} (x + 6)}$

Simplify (9x-45)/(3x^5+24x^4+36x^3)*(x^3-8x^2-20x)/(x^2-15x+50)

Related Questions

Support LCMGCF.com by disabling your adblocker.