Simplify (2x+14)/(x^2+15x+56)*(x^2+3x-40)/(6x)

$\frac{2 x + 14}{x^{2} + 15 x + 56} \cdot \frac{x^{2} + 3 x - 40}{6 x}$

Step 1

Factor $2$ out of $2 x + 14$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 14}{x^{2} + 15 x + 56} \cdot \frac{x^{2} + 3 x - 40}{6 x}$

Factor $2$ out of $14$ .

$\frac{2 x + 2 \cdot 7}{x^{2} + 15 x + 56} \cdot \frac{x^{2} + 3 x - 40}{6 x}$

Factor $2$ out of $2 x + 2 \cdot 7$ .

$\frac{2 (x + 7)}{x^{2} + 15 x + 56} \cdot \frac{x^{2} + 3 x - 40}{6 x}$

Step 2

Factor $x^{2} + 15 x + 56$ 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 $56$ and whose sum is $15$ .

$7, 8$

Write the factored form using these integers.

$\frac{2 (x + 7)}{(x + 7) (x + 8)} \cdot \frac{x^{2} + 3 x - 40}{6 x}$

Step 3

Factor $x^{2} + 3 x - 40$ 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 $- 40$ and whose sum is $3$ .

$- 5, 8$

Write the factored form using these integers.

$\frac{2 (x + 7)}{(x + 7) (x + 8)} \cdot \frac{(x - 5) (x + 8)}{6 x}$

Step 4

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

$\frac{2 (x + 7)}{(x + 7) (x + 8)} \cdot \frac{(x - 5) (x + 8)}{2 (3 x)}$

Cancel the common factor.

$\frac{2 (x + 7)}{(x + 7) (x + 8)} \cdot \frac{(x - 5) (x + 8)}{2 (3 x)}$

Rewrite the expression.

$\frac{x + 7}{(x + 7) (x + 8)} \cdot \frac{(x - 5) (x + 8)}{3 x}$

Cancel the common factor of $x + 8$ .

Factor $x + 8$ out of $(x + 7) (x + 8)$ .

$\frac{x + 7}{(x + 8) (x + 7)} \cdot \frac{(x - 5) (x + 8)}{3 x}$

Factor $x + 8$ out of $(x - 5) (x + 8)$ .

$\frac{x + 7}{(x + 8) (x + 7)} \cdot \frac{(x + 8) (x - 5)}{3 x}$

Cancel the common factor.

$\frac{x + 7}{(x + 8) (x + 7)} \cdot \frac{(x + 8) (x - 5)}{3 x}$

Rewrite the expression.

$\frac{x + 7}{x + 7} \cdot \frac{x - 5}{3 x}$

Multiply $\frac{x + 7}{x + 7}$ by $\frac{x - 5}{3 x}$ .

$\frac{(x + 7) (x - 5)}{(x + 7) (3 x)}$

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{(x + 7) (x - 5)}{(x + 7) (3 x)}$

Rewrite the expression.

$\frac{x - 5}{3 x}$

Simplify (2x+14)/(x^2+15x+56)*(x^2+3x-40)/(6x)

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