Algebra Examples

$\frac{3 x^{2} - 9 x}{2 x^{3}} \cdot \frac{x^{6}}{5 x^{2} - 15 x}$

Step 1

Factor $3 x$ out of $3 x^{2} - 9 x$ .

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Step 1.1

Factor $3 x$ out of $3 x^{2}$ .

$\frac{3 x (x) - 9 x}{2 x^{3}} \cdot \frac{x^{6}}{5 x^{2} - 15 x}$

Step 1.2

Factor $3 x$ out of $- 9 x$ .

$\frac{3 x (x) + 3 x (- 3)}{2 x^{3}} \cdot \frac{x^{6}}{5 x^{2} - 15 x}$

Step 1.3

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

$\frac{3 x (x - 3)}{2 x^{3}} \cdot \frac{x^{6}}{5 x^{2} - 15 x}$

Step 2

Factor $5 x$ out of $5 x^{2} - 15 x$ .

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Step 2.1

Factor $5 x$ out of $5 x^{2}$ .

$\frac{3 x (x - 3)}{2 x^{3}} \cdot \frac{x^{6}}{5 x (x) - 15 x}$

Step 2.2

Factor $5 x$ out of $- 15 x$ .

$\frac{3 x (x - 3)}{2 x^{3}} \cdot \frac{x^{6}}{5 x (x) + 5 x (- 3)}$

Step 2.3

Factor $5 x$ out of $5 x (x) + 5 x (- 3)$ .

$\frac{3 x (x - 3)}{2 x^{3}} \cdot \frac{x^{6}}{5 x (x - 3)}$

Step 3

Combine.

$\frac{3 x (x - 3) x^{6}}{2 x^{3} (5 x (x - 3))}$

Step 4

Multiply $x$ by $x^{6}$ by adding the exponents.

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Step 4.1

Move $x^{6}$ .

$\frac{3 (x^{6} x) (x - 3)}{2 x^{3} (5 x (x - 3))}$

Step 4.2

Multiply $x^{6}$ by $x$ .

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Step 4.2.1

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

$\frac{3 (x^{6} x^{1}) (x - 3)}{2 x^{3} (5 x (x - 3))}$

Step 4.2.2

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

$\frac{3 x^{6 + 1} (x - 3)}{2 x^{3} (5 x (x - 3))}$

Step 4.3

Add $6$ and $1$ .

$\frac{3 x^{7} (x - 3)}{2 x^{3} (5 x (x - 3))}$

Step 5

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

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

Step 5.2

Multiply $x$ by $x^{3}$ .

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Step 5.2.1

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

$\frac{3 x^{7} (x - 3)}{2 (x^{1} x^{3}) (5 (x - 3))}$

Step 5.2.2

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

$\frac{3 x^{7} (x - 3)}{2 x^{1 + 3} (5 (x - 3))}$

Step 5.3

Add $1$ and $3$ .

$\frac{3 x^{7} (x - 3)}{2 x^{4} (5 (x - 3))}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $x^{7}$ and $x^{4}$ .

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Step 6.1.1

Factor $x^{4}$ out of $3 x^{7} (x - 3)$ .

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

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $x^{4}$ out of $2 x^{4} (5 (x - 3))$ .

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

Step 6.1.2.2

Cancel the common factor.

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

Step 6.1.2.3

Rewrite the expression.

$\frac{3 x^{3} (x - 3)}{2 (5 (x - 3))}$

Step 6.2

Cancel the common factor of $x - 3$ .

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Step 6.2.1

Cancel the common factor.

$\frac{3 x^{3} (x - 3)}{2 (5 (x - 3))}$

Step 6.2.2

Rewrite the expression.

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

Step 7

Multiply $2$ by $5$ .

$\frac{3 x^{3}}{10}$