Algebra Examples

$\frac{2 x^{2} + 4 x}{3 x^{3} + 6 x^{2}}$

Step 1

Factor $2 x$ out of $2 x^{2} + 4 x$ .

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Step 1.1

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

$\frac{2 x (x) + 4 x}{3 x^{3} + 6 x^{2}}$

Step 1.2

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

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

Step 1.3

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

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

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

Step 2

Factor $3 x^{2}$ out of $3 x^{3} + 6 x^{2}$ .

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Step 2.1

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

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

Step 2.2

Factor $3 x^{2}$ out of $6 x^{2}$ .

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

Step 2.3

Factor $3 x^{2}$ out of $3 x^{2} (x) + 3 x^{2} (2)$ .

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $3 x^{2} (x + 2)$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $x + 2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{2}{3 x}$

$\frac{2}{3 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$