Pre-Algebra Examples

$\frac{x}{3 x - 21} \cdot \frac{x^{2} - 7 x}{8}$

Step 1

Factor $3$ out of $3 x - 21$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{x}{3 (x) - 21} \cdot \frac{x^{2} - 7 x}{8}$

Step 1.2

Factor $3$ out of $- 21$ .

$\frac{x}{3 x + 3 \cdot - 7} \cdot \frac{x^{2} - 7 x}{8}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot - 7$ .

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

Step 2

Factor $x$ out of $x^{2} - 7 x$ .

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Step 2.1

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

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

Step 2.2

Factor $x$ out of $- 7 x$ .

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

Step 2.3

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

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

Step 3

Cancel the common factor of $x - 7$ .

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Step 3.1

Factor $x - 7$ out of $3 (x - 7)$ .

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

Step 3.2

Factor $x - 7$ out of $x (x - 7)$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$\frac{x}{3} \cdot \frac{x}{8}$

Step 4

Multiply $\frac{x}{3}$ by $\frac{x}{8}$ .

$\frac{x \cdot x}{3 \cdot 8}$

Step 5

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

$\frac{x^{1} x}{3 \cdot 8}$

Step 6

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

$\frac{x^{1} x^{1}}{3 \cdot 8}$

Step 7

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

$\frac{x^{1 + 1}}{3 \cdot 8}$

Step 8

Add $1$ and $1$ .

$\frac{x^{2}}{3 \cdot 8}$

Step 9

Multiply $3$ by $8$ .

$\frac{x^{2}}{24}$