5c/6a^2b+7a/8b^2c-b/12a^2c
=(5/6)c*a^(-2b)+(7/8)a*b^(-2c)-(1/12)b*a^(-2c)
=a^(-2b)*{[(5/6)c]+[(7/8)a^(2b+1)*b^(-2c)]-[(1/12)b*a^(2b-2c)]}
=[a^(-2b)*b^(-2c)]*{[(5/6)c*b^(2c)]+[(7/8)a^(2b+1)]-[(1/12)b^(2c)*a^(2b-2c)]}
=[a^(-2b)*b^(-2c)*a^(-2c)]*{[(5/6)c*b^(2c)*a^(2c)]+[(7/8)a^(2b+2c+1)]-[(1/12)b^(2c)*a^(2b)]}
=[(5/6)(ab)^(2c)*c+(7/8)a^(2b+2c+1)-(1/12)a^(2b)*b^(2c)]/[a^(2b+2c)*b^(2c)]
=[20(ab)^(2c)*c+21a^(2b+2c+1)-2a^(2b)*b^(2c)]/[24a^(2b+2c)*b^(2c)]