Basic Math Examples

$\frac{7}{3 + \sqrt{19}}$

Step 1

Multiply $\frac{7}{3 + \sqrt{19}}$ by $\frac{3 - \sqrt{19}}{3 - \sqrt{19}}$ .

$\frac{7}{3 + \sqrt{19}} \cdot \frac{3 - \sqrt{19}}{3 - \sqrt{19}}$

Step 2

Multiply $\frac{7}{3 + \sqrt{19}}$ by $\frac{3 - \sqrt{19}}{3 - \sqrt{19}}$ .

$\frac{7 (3 - \sqrt{19})}{(3 + \sqrt{19}) (3 - \sqrt{19})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (3 - \sqrt{19})}{9 - 3 \sqrt{19} + \sqrt{19} \cdot 3 - {\sqrt{19}}^{2}}$

Step 4

Simplify.

$\frac{7 (3 - \sqrt{19})}{- 10}$

Step 5

Move the negative in front of the fraction.

$- \frac{7 (3 - \sqrt{19})}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (3 - \sqrt{19})}{10}$

Decimal Form:

$0.95122926 \dots$