A) \[\frac{{{x}^{3}}-{{x}^{2}}+4}{{{x}^{2}}+2}\]
B) \[\frac{{{x}^{3}}+{{x}^{2}}+4}{{{x}^{2}}+2}\]
C) \[\frac{{{x}^{3}}+{{x}^{2}}-4}{{{x}^{2}}+2}\]
D) \[\frac{{{x}^{3}}-{{x}^{2}}-4}{{{x}^{2}}+2}\]
Correct Answer: A
Solution :
Let \[\frac{p(x)}{q(x)}\]be the required rational expression, then \[\frac{p(x)}{q(x)}=\frac{2{{x}^{3}}-{{x}^{2}}+3}{{{x}^{2}}+2}-\frac{{{x}^{3}}-1}{{{x}^{2}}+2}\] \[=\frac{2{{x}^{3}}-{{x}^{2}}+3-{{x}^{3}}+1}{{{x}^{2}}+2}\] \[=\frac{{{x}^{3}}-{{x}^{2}}+4}{{{x}^{2}}+2}\]
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