Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

A.

\(\frac{7}{3}\) - \(\frac{1}{7√2}\)

B.

\(\frac{7}{3}\) + \(\frac{1}{7√2}\)

C.

\(\frac{3}{7}\) - \(\frac{1}{7√2}\)

D.

\(\frac{3}{7}\) + \(\frac{√2}{7}\)

Correct answer is D

Rationalization with conjugate \({3+√2}\)

 \(\frac{1}{3-√2}\)

→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

=  \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)

=  \(\frac{3+√2}{9 - 2}\) →  \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) +  \(\frac{√2}{7}\)