# How do you rationalize the denominator and simplify 3/(t-sqrt2)?

Aug 24, 2017

See a solution process below:

#### Explanation:

To rationalize the denominator, or, in other words, remove the radicals from the denominator, we need to multiply this fraction by the appropriate form of $1$.

We can use this quadratic rule to simplify this expression:

$\left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right) = {\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2}$

$\frac{\textcolor{red}{t} + \textcolor{b l u e}{\sqrt{2}}}{\textcolor{red}{t} + \textcolor{b l u e}{\sqrt{2}}} \times \frac{3}{\textcolor{red}{t} - \textcolor{b l u e}{\sqrt{2}}} \implies \frac{3 \left(\textcolor{red}{t} + \textcolor{b l u e}{\sqrt{2}}\right)}{{\textcolor{red}{t}}^{2} - {\left(\textcolor{b l u e}{\sqrt{2}}\right)}^{2}} \implies$

$\frac{3 t + 3 \sqrt{2}}{{t}^{2} - 2}$