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Simplify \(\frac{(√12-√3)}{(√12+√3)}\)


Question

Simplify \(\frac{(√12-√3)}{(√12+√3)}\)

Options

A) zero

B) 1/3

C) 3/5

D) 1

The correct answer is B.

Explanation:

\(\frac{(\sqrt{12}-\sqrt{3})}{(\sqrt{12}+\sqrt{3})}=\frac{\sqrt{4\times 3}-\sqrt{3}}{\sqrt{4\times 3}+\sqrt{3}}\\=\frac{2\sqrt{3}-\sqrt{3}}{2\sqrt{3}+\sqrt{3}}\\=\frac{\sqrt{3}}{3\sqrt{3}}\\=\frac{1}{3}\)

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Dicussion (1)

  • \(\frac{(\sqrt{12}-\sqrt{3})}{(\sqrt{12}+\sqrt{3})}=\frac{\sqrt{4\times 3}-\sqrt{3}}{\sqrt{4\times 3}+\sqrt{3}}\\=\frac{2\sqrt{3}-\sqrt{3}}{2\sqrt{3}+\sqrt{3}}\\=\frac{\sqrt{3}}{3\sqrt{3}}\\=\frac{1}{3}\)