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\( -5\leq a \leq -1 \leq b \leq 3\)$,  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.

 May 22, 2019
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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

 May 22, 2019
edited by Guest  May 22, 2019

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