Basic Math Examples

$\frac{\frac{7 r s^{3}}{10 t^{3} u}}{\frac{21 s^{4}}{5 t^{4} u^{4}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 r s^{3}}{10 t^{3} u} \cdot \frac{5 t^{4} u^{4}}{21 s^{4}}$

Step 2

Combine.

$\frac{7 r s^{3} (5 t^{4} u^{4})}{10 t^{3} u (21 s^{4})}$

Step 3

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

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Step 3.1

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

$\frac{7 (r s^{3} (5 t^{4} u^{4}))}{10 t^{3} u (21 s^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $10 t^{3} u (21 s^{4})$ .

$\frac{7 (r s^{3} (5 t^{4} u^{4}))}{7 (10 t^{3} u (3 s^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (r s^{3} (5 t^{4} u^{4}))}{7 (10 t^{3} u (3 s^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{r s^{3} (5 t^{4} u^{4})}{10 t^{3} u (3 s^{4})}$

Step 4

Cancel the common factor of $s^{3}$ and $s^{4}$ .

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Step 4.1

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

$\frac{s^{3} (r (5 t^{4} u^{4}))}{10 t^{3} u (3 s^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $s^{3}$ out of $10 t^{3} u (3 s^{4})$ .

$\frac{s^{3} (r (5 t^{4} u^{4}))}{s^{3} (10 t^{3} u (3 s))}$

Step 4.2.2

Cancel the common factor.

$\frac{s^{3} (r (5 t^{4} u^{4}))}{s^{3} (10 t^{3} u (3 s))}$

Step 4.2.3

Rewrite the expression.

$\frac{r (5 t^{4} u^{4})}{10 t^{3} u (3 s)}$

Step 5

Cancel the common factor of $5$ and $10$ .

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Step 5.1

Factor $5$ out of $r (5 t^{4} u^{4})$ .

$\frac{5 (r (t^{4} u^{4}))}{10 t^{3} u (3 s)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $10 t^{3} u (3 s)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $t^{4}$ and $t^{3}$ .

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $u$ out of $2 u (3 s)$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Multiply $2$ by $3$ .

$\frac{r t u^{3}}{6 s}$