№1. Сократите дробь: №2. Представьте в виде дроби: №3. Представьте в виде дроби:

№1. Сократите дробь:

1) $$rac{222p^4q^2}{99p^5q} = rac{2 cdot 3 cdot 37 cdot p^4 cdot q^2}{3 cdot 3 cdot 11 cdot p^4 cdot p cdot q} = rac{2 cdot 37 cdot q}{3 cdot 11 cdot p} = \frac{74q}{33p}$$

2) $$rac{7a}{a^2+5a} = rac{7a}{a(a+5)} = rac{7}{a+5}$$

3) $$rac{7x-7y}{x^2-y^2} = rac{7(x-y)}{(x-y)(x+y)} = rac{7}{x+y}$$

4) $$rac{m^2-2mn+4}{m^3+8} = rac{m^2-2mn+4}{(m+2)(m^2-2m+4)} = rac{1}{m+2}$$

№2. Представьте в виде дроби:

1) $$\frac{y-20}{5y-2} + \frac{4y}{y^2} = \frac{y-20}{5y-2} + \frac{4}{y} = \frac{(y-20)y + 4(5y-2)}{y(5y-2)} = \frac{y^2 - 20y + 20y - 8}{5y^2 - 2y} = \frac{y^2 - 8}{5y^2 - 2y}$$

2) $$\frac{1}{4p+q} - \frac{1}{4p-q} = \frac{(4p-q) - (4p+q)}{(4p+q)(4p-q)} = \frac{4p-q-4p-q}{16p^2 - q^2} = \frac{-2q}{16p^2 - q^2}$$

3) $$\frac{7}{a^2+5a} - \frac{a+5}{7a-3} = \frac{7}{a(a+5)} - \frac{a+5}{7a-3} = \frac{7(7a-3) - (a+5)(a(a+5))}{a(a+5)(7a-3)} = \frac{49a - 21 - (a+5)(a^2+5a)}{a(a+5)(7a-3)} = \frac{49a - 21 - (a^3 + 5a^2 + 5a^2 + 25a)}{a(a+5)(7a-3)} = \frac{49a - 21 - a^3 - 10a^2 - 25a}{a(a+5)(7a-3)} = \frac{-a^3 - 10a^2 + 24a - 21}{a(a+5)(7a-3)}$$

№3. Представьте в виде дроби:

1) $$\frac{28b^6}{c^5} cdot \frac{c^3}{84b^6} = \frac{28b^6c^3}{84b^6c^5} = \frac{28}{84} cdot \frac{b^6}{b^6} cdot \frac{c^3}{c^5} = \frac{1}{3} cdot 1 cdot \frac{1}{c^2} = \frac{1}{3c^2}$$

2) $$30x^2y \div \frac{72xy}{z} = 30x^2y cdot \frac{z}{72xy} = \frac{30x^2yz}{72xy} = \frac{30}{72} \cdot \frac{x^2}{x} \cdot \frac{y}{y} \cdot z = \frac{5}{12}xz$$

3) $$(\frac{a}{2a-b} - \frac{a}{a}) cdot \frac{2a-b}{a} + \frac{b}{a} = (\frac{a}{2a-b} - 1) \cdot \frac{2a-b}{a} + \frac{b}{a} = (\frac{a-(2a-b)}{2a-b}) \cdot \frac{2a-b}{a} + \frac{b}{a} = (\frac{a-2a+b}{2a-b}) \cdot \frac{2a-b}{a} + \frac{b}{a} = (\frac{-a+b}{2a-b}) \cdot \frac{2a-b}{a} + \frac{b}{a} = \frac{b-a}{a} + \frac{b}{a} = \frac{b-a+b}{a} = \frac{2b-a}{a}$$