A) \[-\frac{10}{9}\]
B) \[\frac{5}{4}\]
C) \[-\frac{5}{4}\]
D) \[-\frac{5}{3}\]
Correct Answer: C
Solution :
\[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}=\frac{\left( \frac{{{x}^{2}}}{{{y}^{2}}} \right)+1}{\left( \frac{{{x}^{2}}}{{{y}^{2}}} \right)-1}=\frac{{{\left( \frac{x}{y} \right)}^{2}}+1}{{{\left( \frac{x}{y} \right)}^{2}}-1}\] \[=\frac{{{\left( \frac{1}{3} \right)}^{2}}+1}{\left( \frac{1}{3} \right)-1}=\frac{\frac{10}{9}}{-\frac{8}{9}}=-\frac{5}{4}\]
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