Решение:

1. $$x+\frac{1}{y} = \frac{xy}{y}+\frac{1}{y} = \frac{xy+1}{y}$$
2. $$\frac{1}{a}-a = \frac{1}{a}-\frac{a^2}{a} = \frac{1-a^2}{a}$$
3. $$3a-\frac{a}{4} = \frac{12a}{4}-\frac{a}{4} = \frac{12a-a}{4} = \frac{11a}{4}$$
4. $$5b-\frac{2}{b} = \frac{5b^2}{b}-\frac{2}{b} = \frac{5b^2-2}{b}$$
5. $$\frac{a^2+b}{a}$$ - это уже дробь, упрощать нечего.
6. $$2p-\frac{4p^2+1}{2p} = \frac{4p^2}{2p}-\frac{4p^2+1}{2p} = \frac{4p^2-(4p^2+1)}{2p} = \frac{4p^2-4p^2-1}{2p} = \frac{-1}{2p}$$
7. $$c-\frac{(b+c)^2}{2b} = \frac{2bc}{2b}-\frac{b^2+2bc+c^2}{2b} = \frac{2bc-(b^2+2bc+c^2)}{2b} = \frac{2bc-b^2-2bc-c^2}{2b} = \frac{-b^2-c^2}{2b} = -\frac{b^2+c^2}{2b}$$

Ответы:

1. $$\frac{xy+1}{y}$$
2. $$\frac{1-a^2}{a}$$
3. $$\frac{11a}{4}$$
4. $$\frac{5b^2-2}{b}$$
5. $$\frac{a^2+b}{a}$$
6. $$\frac{-1}{2p}$$
7. $$\frac{-(b^2+c^2)}{2b}$$