Докажите тождество: (c+6)/(c^2-4c+4)∶(c^2-36)/(16c-32)-4/(c-6)=4/(2-c).

\[\frac{16}{(c - 2)(c - 6)} - \frac{4}{c - 6} = \frac{4}{2 - c}\]

\[\frac{16 - 4 \cdot (c - 2)}{(c - 2)(c - 6)} = \frac{4}{2 - c}\]

\[\frac{16 - 4c + 8}{(c - 2)(c - 6)} = \frac{4}{2 - c}\]

\[\frac{24 - 4c}{(c - 2)(c - 6)} = \frac{4}{2 - c}\]

\[\frac{4}{2 - c} = \frac{4}{2 - c}.\]