Algebra Examples

$\frac{\frac{3 x^{2}}{10}}{\frac{9 x^{2}}{4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 x^{2}}{10} \cdot \frac{4}{9 x^{2}}$

Step 2

Combine.

$\frac{3 x^{2} \cdot 4}{10 (9 x^{2})}$

Step 3

Cancel the common factor of $3$ and $9$ .

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Step 3.1

Factor $3$ out of $3 x^{2} \cdot 4$ .

$\frac{3 (x^{2} \cdot 4)}{10 (9 x^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $10 (9 x^{2})$ .

$\frac{3 (x^{2} \cdot 4)}{3 (10 (3 x^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (x^{2} \cdot 4)}{3 (10 (3 x^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} \cdot 4}{10 (3 x^{2})}$

$\frac{x^{2} \cdot 4}{10 (3 x^{2})}$

$\frac{x^{2} \cdot 4}{10 (3 x^{2})}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{2} \cdot 4}{10 (3 x^{2})}$

Step 4.2

Rewrite the expression.

$\frac{4}{10 \cdot (3)}$

$\frac{4}{10 \cdot (3)}$

Step 5

Cancel the common factor of $4$ and $10$ .

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Step 5.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{10 \cdot (3)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $10 \cdot (3)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{2}{5 \cdot 3}$

$\frac{2}{5 \cdot 3}$

$\frac{2}{5 \cdot 3}$

Step 6

Multiply $5$ by $3$ .

$\frac{2}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{15}$

Decimal Form:

$0.1\overline{3}$

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