Question

Выполните сложение и вычитание дробей a) 1/2a+1/a b)3/3-y-y/y^2-9

Answer 1

$\frac{1}{2a} + \frac{1}{a} = \frac{1+1*2}{2a} = \frac{3}{2a} \\ \\ \frac{3}{3-y} - \frac{y}{y^2-9} = \frac{3}{3-y} - \frac{y}{-(3^2-y^2)} = \frac{3}{3-y} -(- \frac{y}{(3-y)(3+y)} )= \\ \\ = \frac{3}{3-y} +\frac{y}{(3-y)(3+y)} = \frac{3(3+y)+y}{(3-y)(3+y)} = \frac{9+3y+y}{9-y^2} = \frac{9+4y}{9-y^2} = \\ \\ = -\frac{4y+9}{y^2-9}$