Simplify (x^2(x+2)(x-4))/(6x(x^2+x-20))

$\frac{x^{2} (x + 2) (x - 4)}{6 x (x^{2} + x - 20)}$

Cancel the common factor of $x^{2}$ and $x$ .

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

$\frac{x ((x (x + 2)) (x - 4))}{6 x (x^{2} + x - 20)}$

Cancel the common factors.

Factor $x$ out of $6 x (x^{2} + x - 20)$ .

$\frac{x ((x (x + 2)) (x - 4))}{x (6 (x^{2} + x - 20))}$

Cancel the common factor.

$\frac{x ((x (x + 2)) (x - 4))}{x (6 (x^{2} + x - 20))}$

Rewrite the expression.

$\frac{(x (x + 2)) (x - 4)}{6 (x^{2} + x - 20)}$

Factor $x^{2} + x - 20$ 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 $1$ .

$- 4, 5$

Write the factored form using these integers.

$\frac{x (x + 2) (x - 4)}{6 ((x - 4) (x + 5))}$

$\frac{x (x + 2) (x - 4)}{6 (x - 4) (x + 5)}$

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{x (x + 2) (x - 4)}{6 (x - 4) (x + 5)}$

Rewrite the expression.

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

Simplify (x^2(x+2)(x-4))/(6x(x^2+x-20))

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