A) \[\frac{a}{a-1}\]
B) \[\frac{a-1}{2}\]
C) \[\frac{2}{a-1}\]
D) \[\frac{2}{1-a}\]
Correct Answer: D
Solution :
\[\frac{{{a}^{1/2}}+{{a}^{-1/2}}}{1-a}+\frac{1-{{a}^{-1/2}}}{1+\sqrt{a}}\] \[=\frac{{{a}^{1/2}}+{{a}^{-1/2}}}{(1+{{a}^{1/2}})\,(1-{{a}^{1/2}})}+\frac{1-{{a}^{-1/2}}}{1+{{a}^{1/2}}}\] \[=\frac{{{a}^{1/2}}+{{a}^{-1/2}}+(1-{{a}^{-1/2}})\,(1-{{a}^{1/2}})}{(1+{{a}^{1/2}})\,(1-{{a}^{1/2}})}\] \[=\frac{{{a}^{1/2}}+{{a}^{-1/2}}+1-{{a}^{-1/2}}-{{a}^{1/2}}+1}{1-a}\] \[=\frac{2}{1-a}\]
You need to login to perform this action.
You will be redirected in
3 sec
