Basic Math Examples

$\frac{- \sqrt{21}}{10} + \frac{\sqrt{3}}{5}$

Step 1

Move the negative in front of the fraction.

$- \frac{\sqrt{21}}{10} + \frac{\sqrt{3}}{5}$

Step 2

To write $\frac{\sqrt{3}}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{\sqrt{21}}{10} + \frac{\sqrt{3}}{5} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{\sqrt{3}}{5}$ by $\frac{2}{2}$ .

$- \frac{\sqrt{21}}{10} + \frac{\sqrt{3} \cdot 2}{5 \cdot 2}$

Step 3.2

Multiply $5$ by $2$ .

$- \frac{\sqrt{21}}{10} + \frac{\sqrt{3} \cdot 2}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{- \sqrt{21} + \sqrt{3} \cdot 2}{10}$

Step 5

Move $2$ to the left of $\sqrt{3}$ .

$\frac{- \sqrt{21} + 2 \sqrt{3}}{10}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- \sqrt{21}$ .

$\frac{- (\sqrt{21}) + 2 \sqrt{3}}{10}$

Step 6.2

Factor $- 1$ out of $2 \sqrt{3}$ .

$\frac{- (\sqrt{21}) - (- 2 \sqrt{3})}{10}$

Step 6.3

Factor $- 1$ out of $- (\sqrt{21}) - (- 2 \sqrt{3})$ .

$\frac{- (\sqrt{21} - 2 \sqrt{3})}{10}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (\sqrt{21} - 2 \sqrt{3})$ as $- 1 (\sqrt{21} - 2 \sqrt{3})$ .

$\frac{- 1 (\sqrt{21} - 2 \sqrt{3})}{10}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{\sqrt{21} - 2 \sqrt{3}}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{21} - 2 \sqrt{3}}{10}$

Decimal Form:

$- 0.11184740 \dots$