If $$x + \frac{1}{x} = 1{\text{,}}$$ then the value of $$\frac{{{x^2} + 3x + 1}}{{{x^2} + 7x + 1}}$$ is?
A. $$\frac{1}{2}$$
B. $$\frac{3}{7}$$
C. 2
D. 3
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given, }}x + \frac{1}{x} = 1 \cr & {\text{Find }}\frac{{{x^2} + 3x + 1}}{{{x^2} + 7x + 1}} \cr & {\text{From equation (i)}} \cr & \Rightarrow x + \frac{1}{x} = 1 \cr & \Rightarrow {x^2} + 1 = x \cr & \Rightarrow \frac{{\left( {{x^2} + 1} \right) + 3x}}{{\left( {{x^2} + 1} \right) + 7x}} \cr & \Rightarrow \frac{{x + 3x}}{{x + 7x}} \cr & \Rightarrow \frac{{4x}}{{8x}} \cr & \Rightarrow \frac{1}{2} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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