Pre-Algebra Examples

$\frac{2 x}{4 x + 2} \cdot \frac{x (14 x + 7)}{6}$

Step 1

Factor $2$ out of $4 x + 2$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$\frac{2 x}{2 (2 x) + 2} \cdot \frac{x (14 x + 7)}{6}$

Step 1.2

Factor $2$ out of $2$ .

$\frac{2 x}{2 (2 x) + 2 (1)} \cdot \frac{x (14 x + 7)}{6}$

Step 1.3

Factor $2$ out of $2 (2 x) + 2 (1)$ .

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x (14 x + 7)}{6}$

Step 2

Factor $7$ out of $14 x + 7$ .

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Step 2.1

Factor $7$ out of $14 x$ .

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x (7 (2 x) + 7)}{6}$

Step 2.2

Factor $7$ out of $7$ .

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x (7 (2 x) + 7 (1))}{6}$

Step 2.3

Factor $7$ out of $7 (2 x) + 7 (1)$ .

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x (7 (2 x + 1))}{6}$

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x \cdot 7 (2 x + 1)}{6}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{2 (2 x + 1)} \cdot \frac{x \cdot 7 (2 x + 1)}{6}$

Step 3.2

Factor $2$ out of $6$ .

$\frac{2 (x)}{2 (2 x + 1)} \cdot \frac{x \cdot 7 (2 x + 1)}{2 (3)}$

Step 3.3

Cancel the common factor.

$\frac{2 x}{2 (2 x + 1)} \cdot \frac{x \cdot 7 (2 x + 1)}{2 \cdot 3}$

Step 3.4

Rewrite the expression.

$\frac{x}{2 (2 x + 1)} \cdot \frac{x \cdot 7 (2 x + 1)}{3}$

Step 4

Cancel the common factor of $2 x + 1$ .

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Step 4.1

Factor $2 x + 1$ out of $2 (2 x + 1)$ .

$\frac{x}{(2 x + 1) \cdot 2} \cdot \frac{x \cdot 7 (2 x + 1)}{3}$

Step 4.2

Factor $2 x + 1$ out of $x \cdot 7 (2 x + 1)$ .

$\frac{x}{(2 x + 1) \cdot 2} \cdot \frac{(2 x + 1) (x \cdot 7)}{3}$

Step 4.3

Cancel the common factor.

$\frac{x}{(2 x + 1) \cdot 2} \cdot \frac{(2 x + 1) (x \cdot 7)}{3}$

Step 4.4

Rewrite the expression.

$\frac{x}{2} \cdot \frac{x \cdot 7}{3}$

Step 5

Multiply $\frac{x}{2}$ by $\frac{x \cdot 7}{3}$ .

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

Step 6

Raise $x$ to the power of $1$ .

$\frac{x^{1} x \cdot 7}{2 \cdot 3}$

Step 7

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1} \cdot 7}{2 \cdot 3}$

Step 8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 1} \cdot 7}{2 \cdot 3}$

Step 9

Add $1$ and $1$ .

$\frac{x^{2} \cdot 7}{2 \cdot 3}$

Step 10

Multiply $2$ by $3$ .

$\frac{x^{2} \cdot 7}{6}$

Step 11

Move $7$ to the left of $x^{2}$ .

$\frac{7 x^{2}}{6}$