Решение:

• a) $$\frac{2a}{51x^6y} \cdot 17x^7y = \frac{2a \cdot 17x^7y}{51x^6y} = \frac{34ax^7y}{51x^6y} = \frac{2ax}{3}$$
• б) $$\frac{24b^2c}{3a^6} : \frac{16bc}{a^5} = \frac{24b^2c}{3a^6} \cdot \frac{a^5}{16bc} = \frac{24b^2ca^5}{48a^6bc} = \frac{b}{2a}$$
• в) $$\frac{5x+10}{x-1} \cdot \frac{x^2-1}{x^2-4} = \frac{5(x+2)}{x-1} \cdot \frac{(x-1)(x+1)}{(x-2)(x+2)} = \frac{5(x+1)}{x-2}$$
• г) $$\frac{y+c}{c} \cdot (\frac{c}{y} - \frac{c}{y+c}) = \frac{y+c}{c} \cdot (\frac{c(y+c) - cy}{y(y+c)}) = \frac{y+c}{c} \cdot \frac{cy + c^2 - cy}{y(y+c)} = \frac{y+c}{c} \cdot \frac{c^2}{y(y+c)} = \frac{c}{y}$$