For what integer values of $y$ is $\frac{3y-1}{y-3}$ an integer?
Write it as $$\frac{3y-1}{y-3}=\frac { 3\left( y-3 \right) +8 }{ y-3 } =3+\frac { 8 }{ y-3 } $$
write $$\frac{3y-1}{y-3}=\frac{3y-9+8}{y-3}=3+\frac{8}{y-3}$$
For what integer values of $y$ is $\frac{3y-1}{y-3}$ an integer?
Write it as $$\frac{3y-1}{y-3}=\frac { 3\left( y-3 \right) +8 }{ y-3 } =3+\frac { 8 }{ y-3 } $$
write $$\frac{3y-1}{y-3}=\frac{3y-9+8}{y-3}=3+\frac{8}{y-3}$$