How do you simplify 7/(3+ sqrt7)?

Mar 14, 2016

See the explanation

Explanation:

Using $\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$

Multiply by 1 but in the form of $1 = \frac{3 - \sqrt{7}}{3 - \sqrt{7}}$

$\frac{7}{3 + \sqrt{7}} \times \frac{3 - \sqrt{7}}{3 - \sqrt{7}}$

$= \frac{7 \left(3 - \sqrt{7}\right)}{{3}^{2} - 7}$

$\frac{7 \left(3 - \sqrt{7}\right)}{9 - 7}$

I will let you finish this off

Hope it helps!