Question

помогите пожалуйста. заранее спасибо с 5 по 8 упростите выражения

Answer 1

$5) \frac{2x-5}{x-2} - \frac{1}{2-x} =\frac{2x-5}{x-2} - \frac{1}{-(x-2)}=\frac{2x-5}{x-2} + \frac{1}{x-2}= \\ \\ = \frac{2x-5+1}{x-2} = \frac{2x-4}{x-2} = \frac{2(x-2)}{x-2} = \frac{2}{1}=2 \\ \\ \\ 6) \frac{a}{2a-b} + \frac{3a-b}{b-2a} = \frac{a}{2a-b} - \frac{3a-b}{2a-b} = \frac{a-(3a-b)}{2a-b} = \\ \\ = \frac{a-3a+b}{2a-b} = \frac{-2a+b}{2a-b} = \frac{-1(2a-b)}{2a-b} = \frac{-1}{1} =-1$

$7) \frac{a}{a^2-9} - \frac{3}{9-a^2} = \frac{a}{a^2-9} - \frac{3}{-(a^2-9)}= \frac{a}{a^2-9}+ \frac{3}{a^2-9}= \\ \\ = \frac{a+3}{a^2-3^2} = \frac{a+3}{(a-3)(a+3)} = \frac{1}{a-3} \\ \\ \\ 8) \frac{y^2}{y-1} + \frac{1}{1-y} = \frac{y^2}{y-1} + \frac{1}{-(y-1)} = \frac{y^2}{y-1} - \frac{1}{y-1}= \\ \\ = \frac{y^2-1}{y-1} = \frac{y^2 -1^2}{y-1} = \frac{(y-1)(y+1)}{y-1} = \frac{y+1}{1} =y+1$