If x + \(\frac{1}{x}\) = 6, then find the value of \(\frac{{3x}}{{2{x^2} - 5x + 2}}\).

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 1)

Answer 1

Given:

x + \(\frac{1}{x}\) = 6

Calculation:

\(\frac{{3x}}{{2{x^2} - 5x + 2}}\)

⇒ \(\frac{3} { \frac {2{x^2} - 5x + 2}{x} }\)

⇒ \(\frac{3} { {2x - 5 + \frac {2}{x}} }\)

⇒ \(\frac{3} { {-5 + 2(x + \frac {1}{x}}) }\)

⇒ \(\frac{3} { {-5 + 2 \times 6} }\)

⇒ \(\frac{3}{7}\)

∴ The value of \(\frac{{3x}}{{2{x^2} - 5x + 2}}\) is \(\frac{3}{7}\).