Question 760668


{{{(z^3 -10z+3)/(z-3)}}}

first factor completely numerator {{{z^3-10z+3}}} ....add {{{-3z^2+3z^2}}}

{{{ z^3-3z^2+3z^2-9z-z+3}}}....group

{{{(z^3-3z^2)+(3z^2-9z)-(z-3)}}}....factor

{{{z^2(z-3)+3z(z-3)-(z-3)}}}

{{{(z^2+3z-1)(z-3)}}}.....now plug it in original equation


{{{((z^2+3z-1)(z-3))/(z-3)}}}....simplify


{{{((z^2+3z-1)cross((z-3)))/cross((z-3))}}}


{{{z^2+3z-1}}}

so, 

{{{(z^3 -10z+3)/(z-3)=z^2+3z-1+0/(z-3)}}}