question_answer

The solution set of the in equation\[\frac{x+11}{x-3}>0\]is

A)  \[(-\infty ,-11)\cup (3,\infty )\]

B)  \[(-\infty ,-10)\cup (2,\infty )\]

C)  \[(-100,-11)\cup (1,\infty )\]

D)  \[(0,5)\cup (-1,0)\]

E)  \[(-5,0)\cup (3,7)\]

Correct Answer: A

Solution :

\[\frac{x+11}{x-3}>0\] \[\Rightarrow \]               \[(x+11)(x-3)>0\] \[\Rightarrow \]               \[x+11>0\]and \[(x-3)>0\]           or            \[x+11<0\]and \[x-3<0\] \[\Rightarrow \]               \[x>-11\]and \[x>3\] or            \[x<-11\]and \[x<3\] \[\Rightarrow \]               \[x<-11\]and \[x>3\] \[\Rightarrow \]               \[x\in (-\infty ,-11)\cup (3,\infty )\]