Question

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

Answer 1

`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}`

Answer 2

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)}}}`