Question

Efectuati: (a+b/a²+a-b/ab²+2ab/a²b²)•a/a+b

Answer 1

amplificam prima fractie cu b², a doua fractie cu a si obtinem:    
[b²(a+b) + a(a-b) + 2ab]/a²b² × a/(a+b) = (ab² + b³ + a² - ab + 2ab)/a²b² × a/(a+b) =    
= (ab² + b³ + a²+ ab)/a²b² × a/(a+b) = [b²(a+b) + a(a+b)]/a²b² × a/(a+b) =  
= (a+b)(b²+a)/a²b² × a/(a+b) = (b²+a)/ab²