A) \[y+\frac{1}{y}\]
B) \[\frac{y}{1+y}\]
C) \[y-\frac{1}{y}\]
D) \[\frac{y}{1-y}\]
Correct Answer: D
Solution :
\[y=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+........\infty \] then \[xy={{x}^{2}}-{{x}^{3}}+{{x}^{4}}-......\infty \] Adding, \[y+xy=x+0+0......+0\] \[\Rightarrow \]\[x-xy=y\Rightarrow x(1-y)=y\Rightarrow x=\frac{y}{1-y}\]. Aliter: \[y=\frac{x}{1-(-x)}\Rightarrow y=\frac{x}{1+x}\] \[\Rightarrow \]\[y+yx=x\Rightarrow x=\frac{y}{1-y}\].
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