Simplify (9x^2-900)/(6x^3+24x^2-360x)*(x^2+3x-54)/(x-10)

$\frac{9 x^{2} - 900}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Step 1

Simplify the numerator.

Factor $9$ out of $9 x^{2} - 900$ .

Factor $9$ out of $9 x^{2}$ .

$\frac{9 (x^{2}) - 900}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $9$ out of $- 900$ .

$\frac{9 x^{2} + 9 \cdot - 100}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $9$ out of $9 x^{2} + 9 \cdot - 100$ .

$\frac{9 (x^{2} - 100)}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

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

$\frac{9 (x^{2} - 10^{2})}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

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 $b = 10$ .

$\frac{9 (x + 10) (x - 10)}{6 x^{3} + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Step 2

Simplify the denominator.

Factor $6 x$ out of $6 x^{3} + 24 x^{2} - 360 x$ .

Factor $6 x$ out of $6 x^{3}$ .

$\frac{9 (x + 10) (x - 10)}{6 x (x^{2}) + 24 x^{2} - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $6 x$ out of $24 x^{2}$ .

$\frac{9 (x + 10) (x - 10)}{6 x (x^{2}) + 6 x (4 x) - 360 x} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $6 x$ out of $- 360 x$ .

$\frac{9 (x + 10) (x - 10)}{6 x (x^{2}) + 6 x (4 x) + 6 x (- 60)} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $6 x$ out of $6 x (x^{2}) + 6 x (4 x)$ .

$\frac{9 (x + 10) (x - 10)}{6 x (x^{2} + 4 x) + 6 x (- 60)} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Factor $6 x$ out of $6 x (x^{2} + 4 x) + 6 x (- 60)$ .

$\frac{9 (x + 10) (x - 10)}{6 x (x^{2} + 4 x - 60)} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

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 $4$ .

$- 6, 10$

Write the factored form using these integers.

$\frac{9 (x + 10) (x - 10)}{6 x ((x - 6) (x + 10))} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

$\frac{9 (x + 10) (x - 10)}{6 x (x - 6) (x + 10)} \cdot \frac{x^{2} + 3 x - 54}{x - 10}$

Step 3

Factor $x^{2} + 3 x - 54$ 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 $- 54$ and whose sum is $3$ .

$- 6, 9$

Write the factored form using these integers.

$\frac{9 (x + 10) (x - 10)}{6 x (x - 6) (x + 10)} \cdot \frac{(x - 6) (x + 9)}{x - 10}$

Step 4

Simplify terms.

Cancel the common factor of $x - 10$ .

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

$\frac{(x - 10) (9 (x + 10))}{6 x (x - 6) (x + 10)} \cdot \frac{(x - 6) (x + 9)}{x - 10}$

Cancel the common factor.

$\frac{(x - 10) (9 (x + 10))}{6 x (x - 6) (x + 10)} \cdot \frac{(x - 6) (x + 9)}{x - 10}$

Rewrite the expression.

$\frac{9 (x + 10)}{6 x (x - 6) (x + 10)} \cdot ((x - 6) (x + 9))$

Cancel the common factor of $x - 6$ .

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

$\frac{9 (x + 10)}{(x - 6) (6 x (x + 10))} \cdot ((x - 6) (x + 9))$

Cancel the common factor.

$\frac{9 (x + 10)}{(x - 6) (6 x (x + 10))} \cdot ((x - 6) (x + 9))$

Rewrite the expression.

$\frac{9 (x + 10)}{6 x (x + 10)} \cdot (x + 9)$

Cancel the common factor of $9$ and $6$ .

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

$\frac{3 (3 (x + 10))}{6 x (x + 10)} \cdot (x + 9)$

Cancel the common factors.

Factor $3$ out of $6 x (x + 10)$ .

$\frac{3 (3 (x + 10))}{3 (2 x (x + 10))} \cdot (x + 9)$

Cancel the common factor.

$\frac{3 (3 (x + 10))}{3 (2 x (x + 10))} \cdot (x + 9)$

Rewrite the expression.

$\frac{3 (x + 10)}{2 x (x + 10)} \cdot (x + 9)$

Cancel the common factor of $x + 10$ .

Cancel the common factor.

$\frac{3 (x + 10)}{2 x (x + 10)} \cdot (x + 9)$

Rewrite the expression.

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

Multiply $\frac{3}{2 x}$ by $x + 9$ .

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

Simplify (9x^2-900)/(6x^3+24x^2-360x)*(x^2+3x-54)/(x-10)

Related Questions

Support LCMGCF.com by disabling your adblocker.