If $\frac{x+y}{xy}=3$  and $\frac{x-y}{xy}=5$ , then the values of x and y are ____ and _____, where  $x\ne 0,y\ne 0.$

$\frac{x+y}{xy}=3$ $\Rightarrow x+y=3xy ....\left(1\right)$

 and $\frac{x-y}{xy}=5$$\Rightarrow x-y=5xy....\left(2\right)$

on adding both the equations we get,

$2x=8xy$

$y=\frac{1}{4}$

substitute $y=\frac{1}{4}$in equation(1), we get

$x+\frac{1}{4}=\frac{3x}{4}$

$x-\frac{3x}{4}=\frac{-1}{4}$

$\frac{x}{4}=\frac{-1}{4}$

$x=-1,and y=\frac{1}{4}$