Question

упростите выражение и найдите его значение при y=3

$frac{y-2}{y^{2}-1} -frac{y-1}{y^{2}+y} =$

$frac{y+1}{y^{2}-4}-frac{y-4}{y^{2}-2y=$

Answer 1

(y-2)/(y^2-1)   -   (y-1)/(y^2+y)=  (y-2)/(y-1)(y+1)   -   (y-1)/y(y+1)=

[(y(y+1)(y-2)-(y-1)(y-1)(y+1)]/y(y-1)(y+1)=(y+1)(y(y+1)-(y-1)^2)/(y(y+1)(y-1)=

 

 = (y+1)(y^2-2y-y^2+2y-1)/y(y-1)(y+1)= (y+1)/y(y+1)(y-1)=1/y(y-1)

 

при у=3 получим 1/6