5. Упростите выражение: a) a2 / a+3 - 9 / a+3 б) y2 / y-2 - 4y-4 / y-2 в) a / a-3 - 2a+1 / 2a-6 г) a-b / 9a : a-b / 9b д) y-5 / y-3 . y²-6y+9 / y2-25

а) $$\frac{a^2}{a+3} - \frac{9}{a+3} = \frac{a^2 - 9}{a+3} = \frac{(a-3)(a+3)}{a+3} = a-3$$

б) $$\frac{y^2}{y-2} - \frac{4y-4}{y-2} = \frac{y^2 - 4y + 4}{y-2} = \frac{(y-2)^2}{y-2} = y-2$$

в) $$\frac{a}{a-3} - \frac{2a+1}{2a-6} = \frac{a}{a-3} - \frac{2a+1}{2(a-3)} = \frac{2a - (2a+1)}{2(a-3)} = \frac{2a-2a-1}{2(a-3)} = \frac{-1}{2(a-3)} = -\frac{1}{2(a-3)}$$

г) $$\frac{a-b}{9a} : \frac{a-b}{9b} = \frac{a-b}{9a} \cdot \frac{9b}{a-b} = \frac{(a-b) \cdot 9b}{9a \cdot (a-b)} = \frac{b}{a}$$

д) $$\frac{y-5}{y-3} \cdot \frac{y^2-6y+9}{y^2-25} = \frac{y-5}{y-3} \cdot \frac{(y-3)^2}{(y-5)(y+5)} = \frac{(y-5)(y-3)^2}{(y-3)(y-5)(y+5)} = \frac{y-3}{y+5}$$

Ответ: а) $$a-3$$, б) $$y-2$$, в) $$\frac{-1}{2(a-3)}$$, г) $$\frac{b}{a}$$, д) $$\frac{y-3}{y+5}$$