Let [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] be three distinct numbers such that:

[tex]\frac{a+b}{a-b}=\frac{b+c}{2(b-c)}=\frac{c+a}{3(c-a)}[/tex]

Find: [tex]8a+9b+5c[/tex]