Basic Math Examples

$\frac{\frac{5 r s^{3}}{21 t^{2} u}}{\frac{15 a^{4}}{7 t^{4} u^{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 r s^{3}}{21 t^{2} u} \cdot \frac{7 t^{4} u^{2}}{15 a^{4}}$

Step 2

Combine.

$\frac{5 r s^{3} (7 t^{4} u^{2})}{21 t^{2} u (15 a^{4})}$

Step 3

Cancel the common factor of $5$ and $15$ .

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Step 3.1

Factor $5$ out of $5 r s^{3} (7 t^{4} u^{2})$ .

$\frac{5 (r s^{3} (7 t^{4} u^{2}))}{21 t^{2} u (15 a^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $21 t^{2} u (15 a^{4})$ .

$\frac{5 (r s^{3} (7 t^{4} u^{2}))}{5 (21 t^{2} u (3 a^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (r s^{3} (7 t^{4} u^{2}))}{5 (21 t^{2} u (3 a^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{r s^{3} (7 t^{4} u^{2})}{21 t^{2} u (3 a^{4})}$

Step 4

Cancel the common factor of $7$ and $21$ .

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Step 4.1

Factor $7$ out of $r s^{3} (7 t^{4} u^{2})$ .

$\frac{7 (r s^{3} (t^{4} u^{2}))}{21 t^{2} u (3 a^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $21 t^{2} u (3 a^{4})$ .

$\frac{7 (r s^{3} (t^{4} u^{2}))}{7 (3 t^{2} u (3 a^{4}))}$

Step 4.2.2

Cancel the common factor.

$\frac{7 (r s^{3} (t^{4} u^{2}))}{7 (3 t^{2} u (3 a^{4}))}$

Step 4.2.3

Rewrite the expression.

$\frac{r s^{3} (t^{4} u^{2})}{3 t^{2} u (3 a^{4})}$

Step 5

Cancel the common factor of $t^{4}$ and $t^{2}$ .

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Step 5.1

Factor $t^{2}$ out of $r s^{3} (t^{4} u^{2})$ .

$\frac{t^{2} (r s^{3} (t^{2} u^{2}))}{3 t^{2} u (3 a^{4})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $t^{2}$ out of $3 t^{2} u (3 a^{4})$ .

$\frac{t^{2} (r s^{3} (t^{2} u^{2}))}{t^{2} (3 u (3 a^{4}))}$

Step 5.2.2

Cancel the common factor.

$\frac{t^{2} (r s^{3} (t^{2} u^{2}))}{t^{2} (3 u (3 a^{4}))}$

Step 5.2.3

Rewrite the expression.

$\frac{r s^{3} (t^{2} u^{2})}{3 u (3 a^{4})}$

Step 6

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

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Step 6.1

Factor $u$ out of $r s^{3} (t^{2} u^{2})$ .

$\frac{u (r s^{3} (t^{2} u))}{3 u (3 a^{4})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $u$ out of $3 u (3 a^{4})$ .

$\frac{u (r s^{3} (t^{2} u))}{u (3 (3 a^{4}))}$

Step 6.2.2

Cancel the common factor.

$\frac{u (r s^{3} (t^{2} u))}{u (3 (3 a^{4}))}$

Step 6.2.3

Rewrite the expression.

$\frac{r s^{3} (t^{2} u)}{3 (3 a^{4})}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{r s^{3} t^{2} u}{3^{2} a^{4}}$

Step 7.2

Raise $3$ to the power of $2$ .

$\frac{r s^{3} t^{2} u}{9 a^{4}}$