Question

xy÷x+y=6÷5 and xy÷y-x=6​

Answer 1

♡⚘✮ʜᴇʏᴀ ᴍᴀᴛᴇ ʜᴇƦᴇ ɪS ʏᴏᴜƦ ᴀɴSᴡᴇƦ :

$\frac{xy}{x + y} = \frac{6}{5} \\ \\ \frac{x + y}{xy} = \frac{5}{6} ...(reverse \: the \: eqn \: ) \\ \\ \frac{x}{xy} + \frac{y}{xy} = \frac{5}{6} \\ \\ \frac{1}{y} + \frac{1}{x} = \frac{5}{6} ...(1). \\ \\ \\ similarly \: \frac{xy}{y - x} = 6 \\ \\ \frac{y - x}{xy} = \frac{1}{6} ...reverse \: the \: eqn \\ \\ \frac{y}{xy} - \frac{x}{xy} = \frac{1}{6} \\ \\ \frac{1}{x} - \frac{1}{y} = \frac{1}{6} ...(2). \\ \\ \\ now \: add \: eqn \: (1)and \: (2) \: \\ \\ \frac{1}{y} + \frac{1}{y} + \frac{1}{x} - \frac{1}{y} \\ \\ \frac{5}{6} + \frac{1}{6} \\ \\ \frac{2}{x} = \frac{5 + 1}{6} \\ \\ \frac{2}{x} = 1 \\ \\ x = 2 \\ \\ \\ substitute \: the \: value \: in \: eqn \: ...(1) \\ \\ \frac{1}{y} + \frac{1}{2} = \frac{5}{6} \\ \\ \frac{1}{y} = \frac{5}{6} - \frac{1}{2} \\ \\ \frac{5 - 3}{6} = \frac{1}{3} \\ \\ y = 3 \\ \\ \\ hence \: x = 2 \: and \: y = 3$

♡ Hope it helps uh Plz maƦk as bƦainliest ♡