Выполните действие: а) \(\frac{x}{y-1}+\frac5{1-y}\); б) \(\frac{a}{c-3}-\frac b{3-c}\); в) \(\frac{2m}{m-n}+\frac{2n}{n-m}\); г) \(\frac{5p}{2q-p}+\frac{10q}{p-2q}\); д) \(\frac{a^2+16}{a-4}+\frac{8a}{4-a}\); е) \(\frac{x^2+9y^2}{x-3y}+\frac{6xy}{3y-x}\).

Используем равенства \(1-y=-(y-1)\), \(3-c=-(c-3)\), \(n-m=-(m-n)\), \(p-2q=-(2q-p)\), \(4-a=-(a-4)\), \(3y-x=-(x-3y)\).

1. \(\frac{x}{y-1}-\frac5{y-1}=\frac{x-5}{y-1}\).
2. \(\frac{a}{c-3}+\frac b{c-3}=\frac{a+b}{c-3}\).
3. \(\frac{2m}{m-n}-\frac{2n}{m-n}=2\).
4. \(\frac{5p}{2q-p}-\frac{10q}{2q-p}=\frac{5(p-2q)}{2q-p}=-5\).
5. \(\frac{a^2+16}{a-4}-\frac{8a}{a-4}=\frac{(a-4)^2}{a-4}=a-4\).
6. \(\frac{x^2+9y^2}{x-3y}-\frac{6xy}{x-3y}=\frac{(x-3y)^2}{x-3y}=x-3y\).

Ответ: а) \(\frac{x-5}{y-1}\); б) \(\frac{a+b}{c-3}\); в) 2; г) −5; д) \(a-4\); е) \(x-3y\).