A) \[\frac{2{{a}^{2}}+3a+7}{{{a}^{2}}+1}\]
B) \[\frac{2{{a}^{2}}-3a+7}{{{a}^{2}}+1}\]
C) \[\frac{2{{a}^{2}}-3a+7}{{{a}^{2}}-1}\]
D) \[\frac{2{{a}^{2}}-3a+9}{{{a}^{2}}-1}\]
Correct Answer: C
Solution :
\[\frac{{{a}^{2}}+2a+3}{{{a}^{2}}-1}+\frac{a-4}{a+1}\] \[=\frac{({{a}^{2}}+2a+3)(a+1)(a-4)({{a}^{2}}-1)}{({{a}^{2}}-1)(a+1)}\] \[=\frac{({{a}^{2}}+2a+\_3)(a+1)+(a-4)(a-1)(a+1)}{(a-1)(a+1)(a+1)}\] \[=\frac{(a+1)\left[ {{a}^{2}}+2a+3+(a-4)(a-1) \right]}{(a-1)(a+1)(a+1)}\] \[=\frac{{{a}^{2}}+2a+3+{{a}^{2}}-5a+4}{(a-1)(a+1)}\] \[=\frac{2{{a}^{2}}-3a+7}{{{a}^{2}}-1}\]
You need to login to perform this action.
You will be redirected in
3 sec
