| If \[x+\frac{1}{x}=1,\] then the value of \[\frac{{{x}^{2}}+3x+1}{{{x}^{2}}+7x+1}\] is [SSC (CGL) Mains 2015] |
A) \[\frac{1}{2}\]
B) \[\frac{3}{7}\]
C) 2
D) 1
Correct Answer: A
Solution :
| Given, \[x+\frac{1}{x}=1\] |
| \[\frac{{{x}^{2}}+3x+1}{{{x}^{2}}+7x+1}\,\,=\,\,\frac{x\left( x+\frac{1}{x} \right)+3x}{x\left( x+\frac{1}{x} \right)+7x}\,\,=\,\,\frac{x+3x}{x+7x}\] |
| \[=\frac{4x}{8x}=\frac{1}{2}=1:2\] |
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