Algebra Examples

$\frac{3 x^{2}}{x + 2} \div \frac{3 x}{x^{2} - 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x^{2}}{x + 2} \cdot \frac{x^{2} - 4}{3 x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3 x$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

$\frac{3 x \cdot x}{x + 2} \cdot \frac{x^{2} - 4}{3 x}$

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Multiply $\frac{x}{x + 2}$ by $x^{2} - 4$ .

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{x (x + 2) (x - 2)}{x + 2}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 2$ .

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Step 4.1.1

Cancel the common factor.

$\frac{x (x + 2) (x - 2)}{x + 2}$

Step 4.1.2

Divide $x (x - 2)$ by $1$ .

$x (x - 2)$

Step 4.2

Apply the distributive property.

$x \cdot x + x \cdot - 2$

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2$

Step 4.3.2

Move $- 2$ to the left of $x$ .

$x^{2} - 2 x$