Simplify \(\rm \frac{{{x^2} + 2x + {y^2}}}{{{x^3} - 5{x^2}}}\) if \(\rm X + \frac{{{y^2}}}{x} = 5\).

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)

Answer 1

Given:

\(\rm X + \frac{{{y^2}}}{x} = 5\)

Calculation:

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

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

⇒ \(\frac{{ {x} + 2 + \frac {y^2}{x} }} {x \times \frac {-y^2}{x}}\) (From given)

⇒ \(\frac{{ 5 + 2}} {-y^2}\) (From given)

⇒ \(\rm -\frac{7}{y^2}\)

∴ The simplified answer is \(\rm -\frac{7}{y^2}\).