A) \[-2\]
B) \[-1\]
C) \[-\frac{2}{7}\]
D) 0
Correct Answer: C
Solution :
We have \[f(x)+g(x)+h(x)=\frac{{{x}^{2}}-4x+17-4x-2}{{{x}^{2}}+x-12}\] \[=\frac{{{x}^{2}}-8x+15}{{{x}^{2}}+x-12}=\frac{(x-3)\,(x-5)}{(x-3)\,(x+4)}\] \[\therefore \,\,\underset{x\to 3}{\mathop{\lim }}\,\,[f(x)+g(x)+h(x)]=\underset{x\to 3}{\mathop{\lim }}\,\,\,\frac{(x-3)\,\,(x-5)}{(x-3)\,\,(x+4)}=-\frac{2}{7}\].
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