Divide ((x^2-3x-28)/(6x))÷((2x-14)/2)

$\frac{x^{2} - 3 x - 28}{6 x} \div \frac{2 x - 14}{2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 3 x - 28}{6 x} \cdot \frac{2}{2 x - 14}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $6 x$ .

$\frac{x^{2} - 3 x - 28}{2 (3 x)} \cdot \frac{2}{2 x - 14}$

Cancel the common factor.

$\frac{x^{2} - 3 x - 28}{2 (3 x)} \cdot \frac{2}{2 x - 14}$

Rewrite the expression.

$\frac{x^{2} - 3 x - 28}{3 x} \cdot \frac{1}{2 x - 14}$

Step 3

Multiply $\frac{x^{2} - 3 x - 28}{3 x}$ by $\frac{1}{2 x - 14}$ .

$\frac{x^{2} - 3 x - 28}{3 x (2 x - 14)}$

Step 4

Factor $x^{2} - 3 x - 28$ 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 $- 28$ and whose sum is $- 3$ .

$- 7, 4$

Write the factored form using these integers.

$\frac{(x - 7) (x + 4)}{3 x (2 x - 14)}$

Step 5

Simplify the denominator.

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

Factor $2$ out of $2 x$ .

$\frac{(x - 7) (x + 4)}{3 x (2 (x) - 14)}$

Factor $2$ out of $- 14$ .

$\frac{(x - 7) (x + 4)}{3 x (2 x + 2 \cdot - 7)}$

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

$\frac{(x - 7) (x + 4)}{3 x (2 (x - 7))}$

$\frac{(x - 7) (x + 4)}{3 x \cdot 2 (x - 7)}$

Multiply $2$ by $3$ .

$\frac{(x - 7) (x + 4)}{6 x (x - 7)}$

Step 6

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{(x - 7) (x + 4)}{6 x (x - 7)}$

Rewrite the expression.

$\frac{x + 4}{6 x}$

Step 7

Split the fraction $\frac{x + 4}{6 x}$ into two fractions.

$\frac{x}{6 x} + \frac{4}{6 x}$

Step 8

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x}{6 x} + \frac{4}{6 x}$

Rewrite the expression.

$\frac{1}{6} + \frac{4}{6 x}$

Step 9

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4$ .

$\frac{1}{6} + \frac{2 (2)}{6 x}$

Cancel the common factors.

Factor $2$ out of $6 x$ .

$\frac{1}{6} + \frac{2 (2)}{2 (3 x)}$

Cancel the common factor.

$\frac{1}{6} + \frac{2 \cdot 2}{2 (3 x)}$

Rewrite the expression.

$\frac{1}{6} + \frac{2}{3 x}$

Divide ((x^2-3x-28)/(6x))÷((2x-14)/2)

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