Question 1115050
<font color="black" face="times" size="3">The LCD is {{{A1*A2*A3}}}. The goal is to get all the fractions to have this denominator so we can combine them. Then we'll apply the reciprocal. 


{{{ 1/(A) = (1)/(A1) + (1)/(A2) + (1)/(A3) }}} Start with the given equation


{{{ 1/(A) = (1*A2*A3)/(A1*A2*A3) + (1)/(A2) + (1)/(A3) }}} Multiply top and bottom of the first fraction by {{{A2*A3}}} 


{{{ 1/(A) = (A2*A3)/(A1*A2*A3) + (1)/(A2) + (1)/(A3) }}} Multiply and simplify


{{{ 1/(A) = (A2*A3)/(A1*A2*A3) + (1*A1*A3)/(A2*A1*A3) + (1)/(A3) }}} Multiply top and bottom of the second fraction by {{{A1*A3}}}


{{{ 1/(A) = (A2*A3)/(A1*A2*A3) + (A1*A3)/(A1*A2*A3) + (1)/(A3) }}} Multiply and simplify


{{{ 1/(A) = (A2*A3)/(A1*A2*A3) + (A1*A3)/(A1*A2*A3) + (1*A1*A2)/(A3*A1*A2) }}} Multiply top and bottom of the third fraction by {{{A1*A2}}}


{{{ 1/(A) = (A2*A3)/(A1*A2*A3) + (A1*A3)/(A1*A2*A3) + (A1*A2)/(A1*A2*A3) }}} Multiply and simplify


{{{ 1/(A) = (A2*A3+A1*A3+A1*A2)/(A1*A2*A3) }}} Add the numerators over the LCD {{{A1*A2*A3}}}


{{{ (A)/(1) = (A1*A2*A3)/(A2*A3+A1*A3+A1*A2) }}} Apply the reciprocal to both sides


{{{ highlight(A = (A1*A2*A3)/(A2*A3+A1*A3+A1*A2)) }}} Simplify
This is the final answer
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