\(\frac{7}{14}+\frac{2}{34}+\frac{-15}{5}+\frac{-6}{51}\) = \(\frac{1}{2}+\frac{1}{17}+\left(-3\right)+\frac{-2}{17}\)
= \(\left[\frac{1}{2}+\left(-3\right)\right]+\left(\frac{1}{17}+\frac{-2}{17}\right)\) = \(\frac{-5}{2}+\frac{-1}{17}=\frac{-87}{34}\)