Algebra Examples

$\frac{6 x^{2}}{x (x - 3)} \cdot \frac{(x - 3)}{10 (x + 2)}$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $6 x^{2}$ .

$\frac{2 (3 x^{2})}{x (x - 3)} \cdot \frac{x - 3}{10 (x + 2)}$

Step 1.2

Factor $2$ out of $10 (x + 2)$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

Cancel the common factor of $x - 3$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Multiply $\frac{3 x^{2}}{x}$ by $\frac{1}{5 (x + 2)}$ .

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

Step 4

Cancel the common factor of $x^{2}$ and $x$ .

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Step 4.1

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

$\frac{x (3 x)}{x (5 (x + 2))}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Cancel the common factor.

$\frac{x (3 x)}{x (5 (x + 2))}$

Step 4.2.2

Rewrite the expression.

$\frac{3 x}{5 (x + 2)}$