Выполните сложение или вычитание дробей: a) 10p/(p-q) + 3p/(q-p); б) 5a/(a-b) + 5b/(b-a); в) (x-3)/(x-1) - 2/(1-x); г) a/(2a-b) + 3a-b/(b-2a); д) (a^2-9)/(a+3); е) y^2/(y-1) + 1/(1-y).

Решение:

1. \(\frac{10p}{p-q} + \frac{3p}{q-p} = \frac{10p}{p-q} - \frac{3p}{p-q} = \frac{10p-3p}{p-q} = \frac{7p}{p-q}\)
2. \(\frac{5a}{a-b} + \frac{5b}{b-a} = \frac{5a}{a-b} - \frac{5b}{a-b} = \frac{5a-5b}{a-b} = \frac{5(a-b)}{a-b} = 5\)
3. \(\frac{x-3}{x-1} - \frac{2}{1-x} = \frac{x-3}{x-1} + \frac{2}{x-1} = \frac{x-3+2}{x-1} = \frac{x-1}{x-1} = 1\)
4. \(\frac{a}{2a-b} + \frac{3a-b}{b-2a} = \frac{a}{2a-b} - \frac{3a-b}{2a-b} = \frac{a-(3a-b)}{2a-b} = \frac{a-3a+b}{2a-b} = \frac{-2a+b}{2a-b} = -1\)
5. \(\frac{a^2-9}{a+3} = \frac{(a-3)(a+3)}{a+3} = a-3\)
6. \(\frac{y^2}{y-1} + \frac{1}{1-y} = \frac{y^2}{y-1} - \frac{1}{y-1} = \frac{y^2-1}{y-1} = \frac{(y-1)(y+1)}{y-1} = y+1\)

Ответ: а) 7p/(p-q); б) 5; в) 1; г) -1; д) a-3; е) y+1.