Simplify (x+4)/(3x)*(4x^2)/(x^2+9x+20)

$\frac{x + 4}{3 x} \cdot \frac{4 x^{2}}{x^{2} + 9 x + 20}$

Factor $x^{2} + 9 x + 20$ 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 $9$ .

$4, 5$

Write the factored form using these integers.

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

Simplify terms.

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3 x} \cdot \frac{4 x^{2}}{x + 5}$

Cancel the common factor of $x$ .

Factor $x$ out of $3 x$ .

$\frac{1}{x \cdot 3} \cdot \frac{4 x^{2}}{x + 5}$

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

$\frac{1}{x \cdot 3} \cdot \frac{x (4 x)}{x + 5}$

Cancel the common factor.

$\frac{1}{x \cdot 3} \cdot \frac{x (4 x)}{x + 5}$

Rewrite the expression.

$\frac{1}{3} \cdot \frac{4 x}{x + 5}$

Multiply $\frac{1}{3}$ by $\frac{4 x}{x + 5}$ .

$\frac{4 x}{3 (x + 5)}$

Simplify (x+4)/(3x)*(4x^2)/(x^2+9x+20)

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