To the OP: depends on what you mean by "simplified." What WolframAlpha gives is
$$
\frac{\sqrt{x^2 + y^2} + y}{y}
$$
which I would further simplify to
$$
\frac{\sqrt{x^2 + y^2}}{y}+1
$$
... or even one more step:
$$
\dfrac{\sqrt{x^2+y^2}}{y}+1=1+\sqrt{\left(\dfrac{x}{y}\right)^2+1}
$$
which gives a nice form with only one variable expression ##z:=\dfrac{x}{y}##.