Question 1136285
{{{t/(ry - 3) = r/y}}}

{{{y(ry-3)(t/(ry-3))=y(ry-3)(r/y)}}}

{{{y(ry-3)(t/(ry-3))=(ry-3)(r)}}}

{{{yt=yr^2-3r}}}

{{{yt-yr^2=-3r}}}

{{{y(t-r^2)=-3r}}}

{{{y(r^2-t)=3r}}}


{{{y=3r/(r^2-t)}}}


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Easier still,
You were instructed to solve for y, which only appears in the denominators.  If the two rational expressions are equal, then their reciprocals are also equal.


{{{(ry-3)/t=y/r}}}


{{{r(ry-3)=ty}}}


{{{r^2y-3r=ty}}}


{{{-3r=ty-r^2y}}}


{{{3r=yr^2-ty}}}


{{{(3r)/(r^2-t)=y}}}