Question

Помогите спростити вирази они на фото

Answer 1

$1); ; Big(frac{a+6}{a^2-4}-frac{2}{a^2+2a}Big):frac{a+2}{a^2-2a}=Big(frac{a+6}{(a-2)(a+2)}-frac{2}{a(a+2)}Big)cdot frac{a(a-2)}{a+2}=\\=frac{a^2+6a-2a+4}{a(a-2)(a+2)}cdot frac{a(a-2)}{a+2}=frac{a^2+4a+4}{a(a-2)(a+2)}cdot frac{a(a-2)}{a+2}=frac{(a+2)^2}{a(a-2)(a+2)}cdot frac{a(a-2)}{a+2}=1$

$2); ; Big(frac{2y+1}{y^2+6y+9}-frac{y-2}{y^2+3y}Big):frac{y^2+6}{y^3-9y}=Big(frac{2y+1}{(y+3)^2}-frac{y-2}{y(y+3)}Big)cdot frac{y(y^2-9)}{y^2+6}=\\=frac{2y^2+y-(y-2)(y+3)}{y(y+3)^2}cdot frac{y(y-3)(y+3)}{y^2+6}=frac{2y^2+y-y^2-y+6}{y(y+3)^2}cdot frac{y(y-3)(y+3)}{y^2+6}=\\=frac{y^2+6}{y+3}cdot frac{y-3}{y^2+6}=frac{y-3}{y+3}$

$3); ; frac{3a}{a-3}+frac{a+5}{6-2a}cdot frac{54}{5a+a^2}=frac{3a}{a-3}+frac{a+5}{-2(a-3)}cdot frac{54}{a(a+5)}=frac{3a}{a-3}-frac{27}{a(a-3)}=\\=frac{3a^2-27}{a(a-3)}=frac{3(a-3)(a+3)}{a(a-3)}=frac{3(a+3)}{a}$