Basic Math Examples

$\frac{2 \cdot (- \frac{21}{20})}{1 - {(\frac{21}{20})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $2$ by $- 1$ .

$\frac{- 2 (\frac{21}{20})}{1 - {(\frac{21}{20})}^{2}}$

Step 1.2

Combine $- 2$ and $\frac{21}{20}$ .

$\frac{\frac{- 2 \cdot 21}{20}}{1 - {(\frac{21}{20})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{21}{20}$ .

$\frac{\frac{- 2 \cdot 21}{20}}{1 - \frac{21^{2}}{20^{2}}}$

Step 2.2

Raise $21$ to the power of $2$ .

$\frac{\frac{- 2 \cdot 21}{20}}{1 - \frac{441}{20^{2}}}$

Step 2.3

Raise $20$ to the power of $2$ .

$\frac{\frac{- 2 \cdot 21}{20}}{1 - \frac{441}{400}}$

Step 2.4

Write $1$ as a fraction with a common denominator.

$\frac{\frac{- 2 \cdot 21}{20}}{\frac{400}{400} - \frac{441}{400}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{- 2 \cdot 21}{20}}{\frac{400 - 441}{400}}$

Step 2.6

Subtract $441$ from $400$ .

$\frac{\frac{- 2 \cdot 21}{20}}{\frac{- 41}{400}}$

Step 2.7

Move the negative in front of the fraction.

$\frac{\frac{- 2 \cdot 21}{20}}{- \frac{41}{400}}$

Step 3

Multiply $- 2$ by $21$ .

$\frac{\frac{- 42}{20}}{- \frac{41}{400}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 42$ and $20$ .

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Step 4.1.1

Factor $2$ out of $- 42$ .

$\frac{\frac{2 (- 21)}{20}}{- \frac{41}{400}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $20$ .

$\frac{\frac{2 \cdot - 21}{2 \cdot 10}}{- \frac{41}{400}}$

Step 4.1.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot - 21}{2 \cdot 10}}{- \frac{41}{400}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{\frac{- 21}{10}}{- \frac{41}{400}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{- \frac{21}{10}}{- \frac{41}{400}}$

Step 5

Dividing two negative values results in a positive value.

$\frac{\frac{21}{10}}{\frac{41}{400}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{21}{10} \cdot \frac{400}{41}$

Step 7

Cancel the common factor of $10$ .

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Step 7.1

Factor $10$ out of $400$ .

$\frac{21}{10} \cdot \frac{10 (40)}{41}$

Step 7.2

Cancel the common factor.

$\frac{21}{10} \cdot \frac{10 \cdot 40}{41}$

Step 7.3

Rewrite the expression.

$21 (\frac{40}{41})$

Step 8

Combine $21$ and $\frac{40}{41}$ .

$\frac{21 \cdot 40}{41}$

Step 9

Multiply $21$ by $40$ .

$\frac{840}{41}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{840}{41}$

Decimal Form:

$20.\overline{48780}$

Mixed Number Form:

$20 \frac{20}{41}$