simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
A
3
B
\(\frac{2}{3}\)
C
7
D
-4
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
L.C.M = (3- 2) (3 + 2)
∴ \(\frac{1}{\sqrt{3 - 2}}\) - \(\frac{1}{\sqrt{3 - 2}}\) = \(\frac{\sqrt{3 + 2} - \sqrt{3 - 2}}{\sqrt{3 - 2} + \sqrt{3 - 2}}\)
\(\frac{√3 + 2 - √3 + 2}{3 - 2√3 + 2√3 - 4}\) = \(\frac{4}{3 - 2}\)
= \(\frac{4}{-1}\)
= -4
Source: Myschool Past Questions Archive (Record #31138)