(2/(x-2)+(3x-21)/(x²+x-6)+2x/(x-3))*x/(2x-5)=x/(x-2)
1)/(x-2)+(3x-21)/(x²+x-6)+2x/(x-3)=(2(x+3)+(3x-21)+2x(x-2))/[(x-2)(x+3)]=
=(2x+6+3x-21+2x²-4x)/[(x-2)(x+3)]=(2x²+x-15)/[(x-2)(x+3)]=
=(2x-5)(x+3)/[(x-2)(x+3)]=(2x-5)/(x-2)
2)(2x-5)/(x-2)*x/(2x-5)=x/(x-2)
(b/(a²-ab)-1/(a-b)):((a+b)/(a²-ab)-b/(ab-b²))=(b-a)/b
1)b/a(a-b)-1/(a-b)=(b-a)/a(a-b)=-1/a
2)(a+b)/a(a-b)-b/b(a-b)=(ab+b²-ab)/[ab(a-b)]=b²/[ab(a-b)]=b/[a(a-b)]
3)-1/a:b/[a(a-b)]=-1/a*a(a-b)/b=(b-a)/b
(1/(4x²-y²:(2x+y)/(y-2x)²-(2x-y)/(4x²+2xy))*(2x+y)²/y²=
1)1/(2x-y)(2x+y)*(2x-y)²/(2x+y)=(2x-y)/(2x+y)²
2)(2x-y)/(2x+y)²-(2x-y)/2x(2x+y)=(2x-y)(2x-2x-y)/[2x(2x+y)²]=
=(2x-y)(-y)/[2x(2x+y)²]
3)y(y-2x)/[2x(2x+y)²]*(2x+y)²/y²=(y-2x)/y