A) \[\frac{1}{{{a}^{2}}+5a+6}\]
B) \[\frac{a+2}{{{a}^{2}}+5a+6}\]
C) \[0\]
D) \[\frac{{{(a+2)}^{2}}}{{{a}^{2}}+5a+6}\]
Correct Answer: A
Solution :
\[\frac{a+2}{a+3}-\frac{(a+1)}{a+2}=\frac{{{(a+2)}^{2}}-(a+1)(a+3)}{(a+3)(a+2)}\] \[=\frac{{{a}^{2}}+4+4a-({{a}^{2}}+4a+3)}{{{a}^{2}}+5a+6}=\frac{1}{{{a}^{2}}+5a+6}\]
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