Question

Помогите упростить выражения:

Answer 1

1)(36-y²)/(y-8) *[y/(y-6) -2y/(y²-12y+36)] + 12y/(y-6)=-y

y/(y-6) -2y/(y-6)²=(y²-6y-2y)/(y-6)²=y(y-8)/(y-6)²
(36-y²)/(y-8) *y(y-8)/(y-6)²=(6-y)(6+y)*y*(y-8)/(y-8)*(6-y)²=y(6+y)/(6-y)
y(6+y)/(6-y)+12y/(y-6)=(6y+y²-12y)/(6-y)=y(y-6)/(6-y)=-y

2)[3x/(x-4) -6x/(x²-8x+16)]:(x-6)/(16-x²) +24x/(x-4)=-3x

3x/(x-4) -6x/(x-4)²=(3x²-12x-6x)/(x-4)²=3x(x-6)/(x-4)²
3x(x-6)/(x-4)²: (x-6)/(16-x²)=3x(x-6)/(4-x)²*(4-x)(4+x)/(x-6)=3x(4+x)/(4-x)
3x(4+x)/(4-x)+24x/(x-4)=(12x+3x²-24x)/(4-x)=3x(x-4)/(4-x)=-3x

3)[(a+b)/(b-a) -(b-a)/(b+a) -4a²/(a²-b²)] : [a²/(b³-ab²) +(a-b)/b²+2/b]=(b+a)/(b²-ab)

(a+b)/(b-a) -(b-a)/(b+a) -4a²/(a²-b²)=(a²+2ab+b²-b²+2ab-a²+4a²)/(b²-a²)=
=4a(a+b)/(b²-a²)
a²/b²(b-a) +(a-b)/b² +2/b=(a²-b²+2ab-a²+2b²-ab)/b²(b-a)=(b²+ab)/b²(b-a)=
=b(b+a)/b²(b-a)=(b+a)/(b²-ab)