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18 votes
18 votes
If a = 1/x+1/y , what is the value of 1/a

User Aanal Shah
by
2.9k points

2 Answers

17 votes
17 votes

Solution


a=(1)/(x)+(1)/(y)

so the value of 1/a is…


\begin{aligned}(1)/(a)&=(1)/((1)/(x)+(1)/(y))\\&\Rightarrow(1)/((y+x)/(xy))\\&\Rightarrow1*(xy)/(y+x)\\&\Rightarrow(xy)/(x+y)\end{aligned}

User Morric
by
2.7k points
10 votes
10 votes

We are given that a =(1/x) + (1/y) , and need to find the value of (1/a) , as a is the sum of two fractions so we can't reciprocal both sides directly without finding their sum and converting them into a single fraction . So , let's start by simplifying a first


{:\implies \quad \sf a=(1)/(x)+(1)/(y)}


{:\implies \quad \sf a=(x+y)/(xy)}

Now , we knows an indentity ;


  • {\boxed{\bf{{\left((a)/(b)\right)}^(-1)=(b)/(a)}}}

Now , raising to the power -1 on both sides :


{:\implies \quad \sf {\left((a)/(1)\right)}^(-1)={\left((x+y)/(xy)\right)}^(-1)}


{:\implies \quad \bf \therefore \quad \underline{\underline{(1)/(a)=(xy)/(x+y)}}}

User LukeFilewalker
by
3.2k points
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