Simplify (x(x^2+8x+12))/(-6(x^2-3x-10))

$\frac{x (x^{2} + 8 x + 12)}{- 6 (x^{2} - 3 x - 10)}$

Step 1

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.

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

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

Step 2

Factor $x^{2} - 3 x - 10$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

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

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

Step 3

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x (x + 6)}{- 6 (x - 5)}$

Step 4

Move the negative in front of the fraction.

$- \frac{x (x + 6)}{6 (x - 5)}$

Simplify (x(x^2+8x+12))/(-6(x^2-3x-10))

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