Вопрос:

Сократите дроби: 1) \(\frac{4a+8b}{4a}\); 2) \(\frac{5x-10y}{3x-6y}\); 3) \(\frac{x^2-25}{2x-10}\); 4) \(\frac{6x^2-3x}{4-8x}\).

Ответ:

  1. \(\frac{4a+8b}{4a}=\frac{4(a+2b)}{4a}=\frac{a+2b}{a}\), \(a
    e0\).
  2. \(\frac{5x-10y}{3x-6y}=\frac{5(x-2y)}{3(x-2y)}=\frac{5}{3}\), \(x
    e2y\).
  3. \(\frac{x^2-25}{2x-10}=\frac{(x-5)(x+5)}{2(x-5)}=\frac{x+5}{2}\), \(x
    e5\).
  4. \(\frac{6x^2-3x}{4-8x}=\frac{3x(2x-1)}{4(1-2x)}=\frac{3x(2x-1)}{-4(2x-1)}=-\frac{3x}{4}\), \(x
    e\frac12\).

Ответ: 1) \(\frac{a+2b}{a}\); 2) \(\frac53\); 3) \(\frac{x+5}{2}\); 4) \(-\frac{3x}{4}\).

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