а)( (1+(a+b)/(a-b) )* (2 -2a/(a+b)) =(a-b+a+b)/(a-b) *(2a+2b -2a)/(a+b)=
(2a/(a-b) ) * (2b/(a+b)) = 4ab/(a²-b²).
----- или ------
( (1+(a+b)/(a-b) )* (2 -2a/(a+b)) =((a-b)/(a-b+(a+b)/(a-b))*(2(a+b)/(a+b) -2a/(a+b)) =
(a-b+a+b)/(a-b) *(2a+2b -2a)/(a+b)= .......
б) (1-(a+3b)/2a)(1/(a+3b) +1/(a-3b)) =
((2a-(a+3b))/2a ) * ( (a -3b+a+3b)/(a-3b)(a+3b) ) =((a-3b)/2a ) * (2a/(a-3b)(a+3b) )=
=1/(a+3b).
в) ( (8a²+2a)/(8a³ -1) - (2a+1)/(4a²+2a+1))*(1+(2a+1)/2a -(4a²+10a)/(4a²+2a))
=( (8a² +2a -(4a² -1))/(2a-1)(4a²+2a+1) ) *( (4a²+2a+(2a+1)² -(4a²+10a)/(2a(2a+1) ) =( (4a² +2a+1)/(2a-1)(4a² +2a+1) )*( (4a²+2a+4a²+4a+1 -4a²-10a)/(2a(2a+1) ) = ( 1/(2a-1) )* ( (4a²-4a+1)/2a(2a+1) ) =( 1/(2a-1) )* ( (2a-1)²/2a(2a+1) )
= (2a-1)/2a(a+1) .
* * * 8a³ -1 =(2a)³ -1³ =(2a-1)(4a²+2a+1) ; 4a²+2a=2a(2a+1) * * *
г) ( (1-x)/(1+x) -(1+x)/(1-x)+4x²/(1-x²) ) : (1/(x² -x³) -(1+x)/x² -1) =
( ((1-x)² -(1+x)² +4x²)/(1-x)(1+x) ) : (1/x²(1 -x) -(1+x)/x² -1) =
(- 4x)/(1+x)): ((1 -(1-x²) -(x² -x³))/x²(1 -x) ) = (- 4x)/(1+x)) : x/(1-x)
=4(x-1)/(x+1). * * * стоит проверить * * *