Question

знайдіть суму і різницю дробів

Answer 1

$\dfrac{ax^2}{10m} + \dfrac{4ax^2}{10m} = \dfrac{ax^2 + 4ax^2}{10m} = \dfrac{5ax^2}{10m} = \dfrac{ax^2}{2m}\\\\\dfrac{ax^2}{10m} - \dfrac{4ax^2}{10m} = \dfrac{ax^2 - 4ax^2}{10m} = -\dfrac{3ax^2}{10m}$

$\dfrac{a + 2}{a(a-5)} + \dfrac{2}{5-a} = \dfrac{a + 2}{a(a-5)} - \dfrac{2}{a-5} = \dfrac{a+2-2a}{a(a-5)} = \dfrac{2-a}{a(a-5)}\\\\\dfrac{a + 2}{a(a-5)} - \dfrac{2}{5-a} = \dfrac{a + 2}{a(a-5)} + \dfrac{2}{a-5} = \dfrac{a+2+2a}{a(a-5)} = \dfrac{3a+2}{a(a-5)}$

$7 + \dfrac{3x^2}{a-x^2} = \dfrac{7a - 7x^2}{a-x^2} + \dfrac{3x^2}{a-x^2} = \dfrac{7a - 7x^2 + 3x^2}{a-x^2} = \dfrac{7a - 4x^2}{a-x^2}\\\\7 - \dfrac{3x^2}{a-x^2} = \dfrac{7a - 7x^2}{a-x^2} - \dfrac{3x^2}{a-x^2} = \dfrac{7a - 7x^2 - 3x^2}{a-x^2} = \dfrac{7a-10x^2}{a-x^2}$