Boberon, докажите тождество: 1. (b³-1/b-1 + b) : b²-1/b-1 = b+1;
2. 1+b/1-b² * (1+b³/1+b - b) = 1-b.

сократите дробь:
a⁴-4/a³+2a
x⁴-4x²+4/x³-2x
x⁴-6x²+9/3x-x³
x²-2x+4/x³+8

1. ((b³-1)/(b-1) + b) :( b²-1)/(b-1 )= ((b-1)*(b²+b+1)/(b-1) + b) :(( b-1)(b+1)/(b-1 )=

(b²+b+1+b) :(b+1)=(b+1)² :(b+1)=b+1;  доказано.

2. (1+b)/(1-b² )* ((1+b³)/(1+b) - b) =((1+b)/((1-b)*(1+b)))* ((1+b)*(1-b+b²)/(1+b) - b) =

(1/(1-b)*)* ((1-b+b²- b) =1*(1-b)²/(1-b)= 1-b. доказано.

сократите дробь:

(a⁴-4)/(a³+2a)=(a²+2)(a²-2)/(a(a²+2))=(a²-2)/a

(x⁴-4x²+4)/(x³-2x)=(x²-2)²/(x*(x²-2))=(x²-2)/x

(x⁴-6x²+9)/(3x-x³)=(3-x²)²/(x*(3-x²))=(3-x²)/x

(x²-2x+4)/(x³+8)=(x²-2x+4)/((x+2)*(x²-2x+4))=1/(x+2)