2022/058) Given $\frac{1}{x} + \frac{1}{y} = \frac{1}{x+y}$ find $\frac{x}{y} + \frac{y}{x}$

Multiply both sides by x+ y to get

$\frac{x+y}{x} + \frac{x+y}{y} = 1$

or $(1+ \frac{y}{x}) + (\frac{x}{y} + 1)  = 1$

or   $\frac{y}{x} +\frac{x}{y} + 2  = 1$

or $\frac{y}{x} + \frac{x}{y}   = -1$