Evaluate the expression A= 1 3+ 5 - 1 3- 5 and express your answer in its simplest form.

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Evaluate the expression A=13+5−13−5A=\frac{1}{3+\sqrt{5}}-\frac{1}{3-\sqrt{5}} and express your answer in its simplest form. (i) Rationalise the denominator of each fraction separately and write them in simplest form. (ii) Subtract the two simplified fractions to obtain the exact value of AA. (iii) Show that the final answer contains no radical in the denominator.

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