Answer
$$f\left( { - 1,2} \right) = - \frac{5}{9}{\text{ and }}f\left( {6, - 3} \right) = - \frac{4}{3}$$
Work Step by Step
$$\eqalign{
& f\left( {x,y} \right) = \frac{{x - 2y}}{{x + 5y}} \cr
& {\text{find }}f\left( { - 1,2} \right).{\text{ substitute }} - 1{\text{ for }}x{\text{ and }}2{\text{ for }}y \cr
& f\left( { - 1,2} \right) = \frac{{ - 1 - 2\left( 2 \right)}}{{ - 1 + 5\left( 2 \right)}} \cr
& {\text{simplifying}} \cr
& f\left( { - 1,2} \right) = \frac{{ - 1 - 4}}{{ - 1 + 10}} \cr
& f\left( { - 1,2} \right) = - \frac{5}{9} \cr
& \cr
& {\text{find }}f\left( {6, - 3} \right).{\text{ substitute 6 for }}x{\text{ and }} - 3{\text{ for }}y \cr
& f\left( {6, - 3} \right) = \frac{{6 - 2\left( { - 3} \right)}}{{6 + 5\left( { - 3} \right)}} \cr
& {\text{simplifying}} \cr
& f\left( {6, - 3} \right) = \frac{{6 + 6}}{{6 - 15}} \cr
& f\left( {6, - 3} \right) = - \frac{4}{3} \cr} $$
