lean_workbook_plus_26561

After making the substitution $x=\frac{1}{a}$, $y=\frac{1}{b}$, and $z=\frac{1}{c}$, we have the system: \n$a+b = \frac{5}{6}$ \n$b+c = \frac{7}{10}$ \n$c+a = \frac{8}{15}$ \nFind the values of $a$, $b$, and $c$.