Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
A
\(\frac{7}{3}\)
B
\(\frac{5}{3}\)
C
\(\frac{5}{2}\)
D
\(\frac{3}{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #29358)