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