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

  • A zero
  • B 1/3
  • C 3/5
  • D 1

The correct answer is B. 1/3

Let's simplify the given expression step by step:

\(\frac{(\sqrt{12} - \sqrt{3})}{(\sqrt{12} + \sqrt{3})}\)

First, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator:

\(\frac{(\sqrt{12} - \sqrt{3})}{(\sqrt{12} + \sqrt{3})} \times \frac{(\sqrt{12} - \sqrt{3})}{(\sqrt{12} - \sqrt{3})} \)

Simplify the numerator and denominator separately:

\(\frac{12 - 2\sqrt{36} + 3}{12 - (\sqrt{3})^2}\)

\( \frac{12 - 2 \cdot 6 + 3}{12 - 3} \)

\(\frac{12 - 12 + 3}{9}\)

\(\frac{3}{9}\)

Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (which is 3):

\(\frac{1}{3} \)

Therefore, the simplified value of the given expression is \(\frac{1}{3}\).

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