Question

先计算1/2+1/3,1/a+1/b,再解决下面的问题：已知1/a+1/b=-4/a+b,求b/a+a/b的值

Answer 1

1/2+1/3=(2+3)/(2*3)=5/6
1/a+1/b=b/ab+a/ab=(a+b)/ab
1/a+1/b=-4/a+b => (a+b)/ab =-4/(a+b) => (a+b)^2=-4ab => a^2+b^2=-6ab
b/a+a/b=b^2/ab+ a^2/ab = (a^2+b^2) /ab = -6ab/ab=-6