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# If and , what is the least possible value of ​? Express your answer as a common fraction.

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If  $$-5\leq a \leq -1$$ 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.

Dec 8, 2020

#1
+127
+1

ay = [-5,-4,-3,-2,-1]
be = [1,2,3]
lo = float('inf')
answr = 0
for a in ay:
for b in be:
if (1/a+1/b)*(1/b-1/a) < lo:
lo = (1/a+1/b)*(1/b-1/a)
answr = [a,b]
print (lo)
print (answr)

Dec 8, 2020

#1
+127
+1

ay = [-5,-4,-3,-2,-1]
be = [1,2,3]
lo = float('inf')
answr = 0
for a in ay:
for b in be:
if (1/a+1/b)*(1/b-1/a) < lo:
lo = (1/a+1/b)*(1/b-1/a)
answr = [a,b]
print (lo)
print (answr)

BWStar Dec 8, 2020