11.11. Представьте в виде алгебраической дроби выражение: 1) 3x^2 / 9x^3 : 5y^3 / 2y^2 : 3(x-1) / 5y 2) 5a(b-1) / 5cd^2 : 9ab / cd^2 : a^2 / (b-1) 3) 7p^5q^2(p+1) / 3p : 14p^4q^4 / 3p : 10q^8 / 7p^5 4) 8x^2y^3 / 7ab : 14xy^2 / 7ab : 2x^2(y+2) / ab

Краткое пояснение:

Решение:

1)

• \[ \frac{3x^2}{9x^3} : \frac{5y^3}{2y^2} : \frac{3(x-1)}{5y} = \frac{3x^2}{9x^3} \cdot \frac{2y^2}{5y^3} \cdot \frac{5y}{3(x-1)} \]
• \[ = \frac{3x^2 \cdot 2y^2 \cdot 5y}{9x^3 \cdot 5y^3 \cdot 3(x-1)} = \frac{30x^2y^3}{135x^3y^3(x-1)} \]
• \[ = \frac{2}{9x(x-1)} \]

2)

• \[ \frac{5a(b-1)}{5cd^2} : \frac{9ab}{cd^2} : \frac{a^2}{(b-1)} = \frac{5a(b-1)}{5cd^2} \cdot \frac{cd^2}{9ab} \cdot \frac{(b-1)}{a^2} \]
• \[ = \frac{5a(b-1)cd^2(b-1)}{5cd^2 \cdot 9ab \cdot a^2} = \frac{5a(b-1)^2cd^2}{45a^3b c d^2} \]
• \[ = \frac{(b-1)^2}{9a^2b} \]

3)

• \[ \frac{7p^5q^2(p+1)}{3p} : \frac{14p^4q^4}{3p} : \frac{10q^8}{7p^5} = \frac{7p^5q^2(p+1)}{3p} \cdot \frac{3p}{14p^4q^4} \cdot \frac{7p^5}{10q^8} \]
• \[ = \frac{7p^5q^2(p+1) \cdot 3p \cdot 7p^5}{3p \cdot 14p^4q^4 \cdot 10q^8} = \frac{147p^{11}q^2(p+1)}{420p^4q^{12}} \]
• \[ = \frac{7p^7(p+1)}{20q^{10}} \]

4)

• \[ \frac{8x^2y^3}{7ab} : \frac{14xy^2}{7ab} : \frac{2x^2(y+2)}{ab} = \frac{8x^2y^3}{7ab} \cdot \frac{7ab}{14xy^2} \cdot \frac{ab}{2x^2(y+2)} \]
• \[ = \frac{8x^2y^3 \cdot 7ab \cdot ab}{7ab \cdot 14xy^2 \cdot 2x^2(y+2)} = \frac{56x^2y^3a^2b}{196x^3y^2ab(y+2)} \]
• \[ = \frac{2y a}{7x(y+2)} \]

Ответ: 1) \[ \frac{2}{9x(x-1)} \]; 2) \[ \frac{(b-1)^2}{9a^2b} \]; 3) \[ \frac{7p^7(p+1)}{20q^{10}} \]; 4) \[ \frac{2ya}{7x(y+2)} \]