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1. (42a³ -30a²b)/(25b³-35ab) =6a²(5b-7a)/5b²(5b - 7a) = - (6/5)* (a/b)² .
2.
1) (a² +b²)/(a² -b²) +b/(b-a) -b /(b+a) =(a² +b²)/(a² -b²) -b(1/(a-b)+1 /(a+b) ) =
(a² +b²)/(a² -b²) -b(a+b +a-b)/(a² -b²) =(a² +b²)/(a² -b²) -2ab/(a² -b²) =
(a² +b² -2ab)/(a² -b²) = (a-b)²/(a-b)(a+b) =(a-b)/(a+b) .
2) (x² +xy+y²)/(x³+3xy(x+y) +y³) * (x² -y²)/(x³-y³) =
(x² +xy+y²)(x² -y²)/(x³+3xy(x+y) +y³)(x³-y³) =
(x² +xy+y²)(x -y)(x+y)/(x+y)³)(x-y)(x² +xy+y²) =1/(x+y)² .
* * *(x² +xy+y²) / (x+y)³ * (x -y)(x+y) / (x-y)(x² +xy+y²) = (x² +xy+y²)/(x+y)³ * (x+y)/(x² +xy+y²) =
(x² +xy+y²)(x+y) / (x+y)³ (x² +xy+y²) = 1/(x+y)². * * *
2.
1) (a² +b²)/(a² -b²) +b/(b-a) -b /(b+a) =(a² +b²)/(a² -b²) -b(1/(a-b)+1 /(a+b) ) =
(a² +b²)/(a² -b²) -b(a+b +a-b)/(a² -b²) =(a² +b²)/(a² -b²) -2ab/(a² -b²) =
(a² +b² -2ab)/(a² -b²) = (a-b)²/(a-b)(a+b) =(a-b)/(a+b) .
2) (x² +xy+y²)/(x³+3xy(x+y) +y³) * (x² -y²)/(x³-y³) =
(x² +xy+y²)(x² -y²)/(x³+3xy(x+y) +y³)(x³-y³) =
(x² +xy+y²)(x -y)(x+y)/(x+y)³)(x-y)(x² +xy+y²) =1/(x+y)² .
* * *(x² +xy+y²) / (x+y)³ * (x -y)(x+y) / (x-y)(x² +xy+y²) = (x² +xy+y²)/(x+y)³ * (x+y)/(x² +xy+y²) =
(x² +xy+y²)(x+y) / (x+y)³ (x² +xy+y²) = 1/(x+y)². * * *
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