若1/a+1/b=3,1/ab=1/4,则(a+b)/a+b=多少

Question

若1/a+1/b=3,1/ab=1/4,则(a+b)/a+b=多少

Answer 1

1/a+1/b=3,则a^2+b^2=3a^2b^2 1/ab=1/4,即ab=4 所以a^2+b^2=3a^2b^2=3*16=48 故(a+b)/a+b=(a^2+b^2+2ab)/(a^2+b^2)=(48+8)/48=56/48=14/12=7/6