Сократить (a^2-3a-1/a+3)* 1/a^2-1*(a^2+a) !

^2 означает квадрат (степень)

(a^2-1)/a^2-((a^2-9)/a)*(1/(a+3))=-(3a+1)/a^2

1)((a^2-9)/a)*(1/(a+3))=((a-3)(a+3)/a)*(1/(a+3))=(a-3)/a

2)(a^2-1)/a^2-(a-3)/a=(a^2-1-a(a+3))/a^2=(a^2-1-a^2-3a)/a^2=-(3a+1)/a^2

((x-y)/(x+y)-(x+y)/(x-y)):(4/(x^2-y^2)=-xy

1)(x-y)/(x+y)-(x+y)/(x-y)=((x-y)^2-(x+y)^2)/(x-y)(x+y)=(x^2-2xy+y^2-x^2-2xy-y^2)/(x^2-y^2)=-4xy/(x^2-y^2)

2)-4xy/(x^2-y^2):(4/(x^2-y^2))=-4xy/(x^2-y^2)*((x^2-y^2)/4)=-xy