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. \[\frac{ab}{a+b}\frac{\frac{x}{(x+y)}\times \frac{y}{\left( x-y \right)}}{\frac{x}{\left( x+y \right)}+\frac{y}{\left( x-y \right)}}\] \[=\frac{xy}{{{x}^{2}}-xy+xy+{{y}^{2}}}=\frac{xy}{{{x}^{2}}+{{y}^{2}}}\]
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