A) \[\frac{1}{4}\]
B) \[\frac{1}{2}\]
C) \[\frac{3}{4}\]
D) 0
Correct Answer: B
Solution :
Expression \[=\frac{{{x}^{4}}-\frac{1}{{{x}^{2}}}}{3{{x}^{2}}+5x-3}\] Dividing numerator and donator by \[x\], \[=\frac{{{x}^{3}}-\frac{1}{{{x}^{3}}}}{3x+5-\frac{3}{x}}=\frac{{{x}^{3}}-\frac{1}{{{x}^{3}}}}{3\left( x-\frac{1}{x} \right)+5}\] \[=\frac{{{\left( x-\frac{1}{x} \right)}^{3}}+3\left( x-\frac{1}{x} \right)}{3\left( x-\frac{1}{x} \right)+5}\] \[=\frac{1+3}{3+5}=\frac{4}{8}=\frac{1}{2}\]
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