Simplify \(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
A
\(\frac{1}{3}\)
B
9
C
16cm
D
3
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
\(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
\(\therefore \frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}} = \frac{2\sqrt{3} - \sqrt{3}}{2\sqrt{3} + \sqrt{3}}\)
= \(\frac{\sqrt{3}}{3\sqrt{3}}\)
= \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #30881)