Question

If a and b are positive integers and their product is 3 times their sum, what is the value of (1/a) + (1/b)?

Answer 1

\[ab = 3(a+b)\]

Answer 2

I know how to set up the equation... I need help with the algebra LOL.

Answer 3

ab=3(a+b) ==> a=3(a+b)/b ===> (1/a) + (1/b) = 1/[3(a+b)/b+1/b = b/3(a+b) + 1/b = [b^2+3a+3v]/[3ab+3b^2]

Answer 4

Sorry but I can't read it... do you mind drawing it out? ><

Answer 5

ok

Answer 6

\[ab=3(a+b) ==> a=3(a+b)/b ===>\] \[(1/a) + (1/b) = 1/[3(a+b)/b+1/b\]\[ = b/3(a+b) + 1/b = [b^2+3a+3v]/[3ab+3b^2]
\]

Answer 7

you may expand the bracjets also

Answer 8

It's SAT math, so the answer has numerical digits :'( It's the free response.

Answer 9

\[\frac{1}{a}+\frac{1}{b}=\frac{-3}{3b-ab}-\frac{3}{3a-ab}\]

Answer 10

sin ab=3(a+b)
divide ab on both side
so (1/a+1/b)=1/3

Answer 11

Thank you.