Question

若a^2+b^2=3ab,求分式(1+2b^2/a^2-b^2)(1+2b/a-b)的值

若a^2+b^2=3ab,求分式(1+2b^2/a^2-b^2)(1+2b/a-b)的值

Answer 1

解：原式=（a²-b²+2b²)/(a²-b²)×(a-b+2b)/(a-b)=(a²+b²)/(a²-b²)×(a+b)/(a-b)=(a²+b²)/(a-b)²
=(a²+b²)/(a²+b²-2ab)
∵a^2+b^2=3ab
∴原式=（3ab)/(3ab-2ab)=3

Answer 2

解;[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]=(a^2-b^2+2b^2)*(a-b+2b)/[(a^2-b^2)(a-b)]
=(a^2+b^2)/(a^2-2ab+b^2)=3ab/ab=3