+31 \( -5\leq a \leq -1 \leq b \leq 3\)$, and \(1 \leq b \leq 3\)what is the least possible value of \(\displaystyle\left(\frac{1}{a}+\frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right)\) $? Express your answer as a common fraction.
a=-5; b=1;c= (1/a+1/b)*(1/b-1/a);printc, a, b; a++;if(a<-1, goto2, 0);a=-5;b++;if(b<3, goto2, discard=0;
The following are all the possible values:
24 / 25 with a = -5 and b = 1
15 / 16 with a = -4 and b = 1
8 / 9 with a = -3 and b = 1
3 / 4 with a = -2 and b = 1
21 / 100 with a = -5 and b = 2
3 / 16 with a = -4 and b =2
5 / 36 with a = -3 and b =2
0 with a = -2 and b =2
-3 / 4 with a = -1 and b = 2
16 / 225 with a = -5 and b =3
7 / 144 with a = -4 and b =3
0 with a =-3 and b =3
-5 / 36 with a = -2 and b =3
-8 / 9 with a = -1 and b = 3
