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