Question

if x-1/y=6 and y-1/x=8 find y/x+x/y​

Answer 1

$x - \dfrac{1}{y} = 6$

$\dfrac{xy - 1}{y} = 6$

$xy - 1 = 6y \: \: \: \: ...(i)$

$y - \dfrac{1}{x} = 8$

$\dfrac{xy - 1}{x} = 8$

$xy - 1 = 8x \: \: \: \: ...(ii)$

As L.H.S. are equal, in both the Equations,

So, due to Equality, their R.H.S. must also be equal.

$8x = 6y$

$\implies \dfrac{x}{y} = \dfrac{3}{4}$

$\implies \dfrac{y}{x} = \dfrac{4}{3}$

Hence,

$\dfrac{y}{x} + \dfrac{x}{y} = \dfrac{4}{3} + \dfrac{3}{4} = \dfrac{16 + 9}{12}$

$\boxed{\dfrac{y}{x} + \dfrac{x}{y} = \dfrac{25}{12} }$