Question

вычислите сложение и вычитание дробей:
1)7у+4/8у-2у+3/6у
2)2-3у/у²-9-5-2у/3-у​

Answer 1

$\dfrac{7y+4}{8y} - \dfrac{2y+3}{6y} = \dfrac{3(7y+4)}{3\cdot8y} - \dfrac{4(2y+3)}{4\cdot6y} = \dfrac{21y+12}{24y} - \dfrac{8y+12}{24y} = \dfrac{21y+12-8y-12}{24y} = \dfrac{13y}{24y} = \dfrac{13}{24}$

$\dfrac{2-3y}{y^2-9} - \dfrac{5-2y}{3-y} = \dfrac{2-3y}{(y-3)(y+3)} - \dfrac{2y-5}{y-3} = \dfrac{2-3y}{(y-3)(y+3)} - \dfrac{(2y-5)(y+3)}{(y-3)(y+3)} = \dfrac{(2-3y) - (2y-5)(y+3)}{(y-3)(y+3)} = \dfrac{2 - 3y - 2y^2 - 6y + 5y + 15}{y^2-9} = \dfrac{-2y^2 - 4y + 17}{y^2-9}$