Упростите выражение: (c+1)/(2c^2-24c+72)-1/(7c-42).

Ответ:

\[\frac{c + 1}{2c^{2} - 24c + 72} - \frac{1}{7c - 42} =\]

\[= \frac{c + 1^{\backslash 7}}{2 \cdot (c - 6)^{2}} - \frac{1^{\backslash 2(c - 6)}}{7 \cdot (c - 6)} =\]

\[= \frac{7 \cdot (c + 1) - 2 \cdot (c - 6)}{14 \cdot (c - 6)^{2}} =\]

\[= \frac{7c + 7 - 2c + 12}{14 \cdot (c - 6)^{2}} =\]

\[= \frac{5c + 19}{14 \cdot (c - 6)^{2}}\]