Question

if x + 1/x = 5 find the value of x/(x^2 + x + 1)​

Answer 1

Answer:

-1 or 4/21

Step-by-step explanation:

$here \: \\ x + \frac{1}{x} = 5 \\ = > \frac{x {}^{2} + 1 }{x} = 5 \\ = > x {}^{2} + 1 = 5x \\ = > x {}^{2} - 5x = - 1 \\ = > x(x - 5) = - 1 \\ = > x = - 1 \: or \: \: x = 4 \\ if \: x = - 1 \: \: then \\ \frac{x}{x {}^{2} + x + 1 } = \frac{ - 1}{1 - 1 + 1} \\ = \frac{ - 1}{1} = - 1 \\ if \: x = 4 \: then \: \\ \frac{x}{x {}^{2} + x + 1 } = \frac{4}{4 {}^{2} + 4 + 1 } \\ = \frac{4}{16 + 4 + 1} = \frac{4}{21}$