A) \[-16\]
B) \[-6\]
C) \[6\]
D) \[8\]
Correct Answer: B
Solution :
\[\frac{x+1}{x-1}+\frac{x+2}{x-2}=\frac{22x+30}{11x-18}\] \[\Rightarrow \] \[\frac{x+1}{x-1}-1+\frac{x+2}{x-2}-1=\frac{22x+30}{11x-18}-2\] \[\Rightarrow \] \[\frac{x+1-x+1}{x-1}+\frac{x+2-x+2}{x-2}\] \[\frac{22x+30-22x+36}{11x-18}\] \[\Rightarrow \] \[\frac{2}{x-1}+\frac{4}{x-2}=\frac{66}{11x-18}\] \[\frac{2(x-2)+4(x-1)}{(x-1)(x-2)}=\frac{66}{11x-18}\] \[\Rightarrow \] \[(6x-8)(11x-18)\] \[\Rightarrow \] \[66({{x}^{2}}-3x+2)\] \[\Rightarrow \] \[66{{x}^{2}}-196x+144\] \[\Rightarrow \] \[66{{x}^{2}}-198x+132\] \[\Rightarrow \] \[198x-196x=132-144\] \[\Rightarrow \] \[2x=-12\] \[\therefore \] \[x=-6\]
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