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Question 126
What is the Simplified value of:
$$\frac{1}{8}\left\{\left(x + \frac{1}{y}\right)^2 - \left(x - \frac{1}{y}\right)^2\right\}$$
Solution
Expression : $$\frac{1}{8}\left\{\left(x + \frac{1}{y}\right)^2 - \left(x - \frac{1}{y}\right)^2\right\}$$
=Â $$\frac{1}{8}\left\{\left(x^2 + \frac{1}{y^2}+\frac{2x}{y}\right) - \left(x^2 + \frac{1}{y^2}-\frac{2x}{y}\right)\right\}$$
= $$\frac{1}{8}\times\frac{4x}{y}=\frac{x}{2y}$$
=> Ans - (A)
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