\[\frac{y + c}{c} \cdot \left( \frac{c^{\backslash y + c}}{y} - \frac{c^{\backslash y}}{y + c} \right) =\]
\[= \frac{y + c}{c} \cdot \frac{yc + c^{2} - yc}{y(y + c)} = \frac{c^{2}}{\text{yc}} = \frac{c}{y}.\]