Question 88

What is the value of $$\frac{1+a}{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}-\frac{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}{1+a}+a^{\frac{-1}{2}}$$ ?

Solution

Expression : $$\frac{1+a}{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}-\frac{a^{\frac{1}{2}}+a^{\frac{-1}{2}}}{1+a}+a^{\frac{-1}{2}}$$

= $$(\frac{1+a}{\sqrt{a}+\frac{1}{\sqrt{a}}})-(\frac{\sqrt{a}+\frac{1}{\sqrt{a}}}{1+a})+(\frac{1}{\sqrt{a}})$$

= $$(\frac{1+a}{\frac{1+a}{\sqrt{a}}})-(\frac{\frac{1+a}{\sqrt{a}}}{1+a})+(\frac{1}{\sqrt{a}})$$

= $$\sqrt{a}-\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{a}}=\sqrt{a}$$

=> Ans - (A)

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