A) \[\frac{2{{y}^{2}}}{{{y}^{2}}-{{x}^{2}}}\]
B) \[\frac{2{{x}^{2}}}{{{y}^{2}}-{{x}^{2}}}\]
C) \[\frac{2{{y}^{2}}}{{{y}^{2}}+{{z}^{2}}}\]
D) \[\frac{2{{x}^{2}}}{{{y}^{2}}+{{x}^{2}}}\]
Correct Answer: A
Solution :
(a): \[\frac{{{x}^{-1}}}{{{x}^{-1}}+{{y}^{-1}}}+\frac{{{x}^{-1}}}{{{x}^{-1}}-{{y}^{-1}}}\Rightarrow \frac{\frac{1}{x}}{\frac{1}{x}+\frac{1}{y}}+\frac{\frac{1}{x}}{\frac{1}{x}-\frac{1}{y}}\] \[\Rightarrow \frac{\frac{1}{x}\times xy}{x+y}+\frac{\frac{1}{x}\times xy}{x-y}\Rightarrow \frac{y}{y+x}-\frac{y}{y-x}\Rightarrow \frac{2{{y}^{2}}}{{{y}^{2}}-{{x}^{2}}}\]
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