Упростите выражение: a) x/(y-1) + 5/(1-y); б) a/(c-3) - 6/(3-c); в) 2m/(m-n) + 2n/(n-m); г) 5p/(2q-p) + 10q/(p-2q); д) (a^2+16)/(a-4) + (a^2+9y^2)/(x-3y).

Решение:

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

Ответ: а) (x-5)/(y-1); б) (a+6)/(c-3); в) 2; г) -5; д) (a^2+16)/(a-4) + (x^2+9y^2)/(x+y)^2.