Question

Спростить вирази они на фото

Answer 1

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

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

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