Given that \(\frac{a}{25-a}+\frac{b}{65-b}+\frac{c}{60-c}=7\), evaluate \(\frac{5}{25-a}+\frac{13}{65-b}+\frac{12}{60-c}\).

Notice that 25 = 5*5, 65 = 13*5, 60 = 12*5. One simple way is then as follows:

Other choices are possible for a, b and c, but they all lead to the same final result.