Find the value of the expression: \(\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?\)
Solution
Correct Answer: Option A
Given expression is,
\(\begin{array}{l} \frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }}\\ = \;\frac{{{{\left( {3\; + \;\sqrt 5 } \right)}^2} - \;{{\left( {3\; - \;\surd 5} \right)}^2}}}{{\left( {3\; - \;\sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)}}\\ = \;\frac{{\left( {9\; + \;5\; + \;6\sqrt 5 } \right) - \;\left( {9\; + \;5\; - 6\;\sqrt 5 } \right)}}{{{{\left( 3 \right)}^2} - \;{{\left( {\sqrt 5 } \right)}^2}}}\\ = \frac{{12\;\sqrt 5 }}{{9 - 5}} \end{array}\)
= 12√5/4
= 3√5
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