The first one $\frac{xy^{2}+y}{y^{2}}$ :

It can also be written as $\frac{y(xy+1)}{y^{2}}$ so :

$x = x*y$

$x = x+1$

$x = x*y$

$y = y*y$

$x = x/y$ , (There is another solution try to find it.)

The second one $3xy+2x^{3}$ :

Tt can also be written as $x(3y+2x^{2})$ so :

$y = y*3$

$x = x*x$

$x = x*2$

$y = x+y$

$x = x/2$

$x = \sqrt{x}$

$x = x*y$

The third one $\frac{5x^{2}+5xy}{x+y}$ :

It can also be written as $\frac{5x(x+y)}{x+y}$ = $5x$ so :

$x = x*5$

The fourth one $\frac{5x^{2}+3xy}{x+y}$ :

Here comes the trick $\frac{5x^{2}+3xy}{x+y}$ = $\frac{2x^{2}+3x^{2}+3xy}{x+y}$ = $\frac{2x^2+3x(x+y)}{x+y}$ = $\frac{2x^{2}}{x+y}+3x$ :

$y = x+y$

$x = x*x$

$x = x*2$

$y = x/y$

$x = x/2$

$x = \sqrt{x}$

$x = x*3$

$y = y+x$

thanks for reading ;)