A) \[\frac{xy}{{{x}^{2}}+{{y}^{2}}}\]
B) \[\frac{{{x}^{2}}+{{y}^{2}}}{xy}\]
C) \[\frac{x}{x+y}\]
D) \[{{\left( \frac{y}{x+y} \right)}^{2}}\]
E) None of these
Correct Answer: A
Solution :
Explanation Option [a] is correct. \[\frac{ab}{a+b}=\frac{\frac{x}{(x+y)}\times \frac{y}{(x-y)}}{\frac{x}{(x+y)}+\frac{y}{(x-y)}}\] \[=\frac{xy}{{{x}^{2}}-xy+xy+{{y}^{2}}}=\frac{xy}{{{x}^{2}}+{{y}^{2}}}\]
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