If $x + \frac{1}{x} = 6$, what is the value of $\frac{x^2 - x + 1}{x^2 + x + 1}$?
Options:
- A: $\frac{3}{4}$
- B: $\frac{5}{7}$
- C: $\frac{4}{5}$
- D: $\frac{1}{2}$
Related Practice Questions:
- Given below are two statements, one labeled as Assertion (A) and the other labeled as Reason (R): Assertion (A): The Cabinet Mission Plan of $1946$ officially recommended the immediate partition of India into two separate sovereign nations. Reason (R): The Mission concluded that a separate state of Pakistan would not solve the communal minority problem and would create serious defense and communication complications. In the context of the above statements, which of the following is correct?
- Who was the Premier of Bengal during the Direct Action Day riots in $August \text{ } 1946$$, who faced severe criticism for his administration's failure to control the violence?
- In which of the following districts of East Bengal did Mahatma Gandhi spend nearly $4$ months from $November \text{ } 1946$ to $March \text{ } 1947$ to restore communal harmony after the outbreak of horrific riots?
- Given below are two statements, one labeled as Assertion (A) and the other labeled as Reason (R): Assertion (A): The Muslim League withdrew its acceptance of the Cabinet Mission Plan on $29 \text{ July } 1946$ and passed the 'Direct Action' resolution. Reason (R): Jawaharlal Nehru's press conference on $10 \text{ July } 1946$ stated that the Congress was completely free to change or modify the Cabinet Mission Plan in the Constituent Assembly. In the context of the above statements, which of the following is correct?