Question

Обчислити
1. 2a+5b/ab - 2a-3b/ab,
2. 5y/y^2-9 - 15/y^2-9
3. y^2+8y/4-y^2 - 4y-4/4-y^2

Answer 1

$\frac{2a+5b}{ab}-\frac{2a-3b}{ab}=\frac{2a+5b-2a+3b}{ab}=\frac{8b}{ab}=\frac{8}{a}\\\\\\\frac{5}{y^2-9}-\frac{15}{y^2-9}=\frac{5y-15}{(y-3)(y+3)}=\frac{5\, (y-3)}{(y-3)(y+3)}=\frac{5}{y+3}\\\\\\\frac{y^2+8y}{4-y^2}-\frac{4y-4}{4-y^2}=\frac{y^2+8y-4y+4}{4-y^2}=\frac{y^2+4y+4}{(2-y)(2+y)}=\frac{(y+2)^2}{(2-y)(y+2)}=\frac{y+2}{2-y}$