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Question
When simplified \[( x^{- 1} + y^{- 1} )^{- 1}\] is equal to
Options
xy
x+y
\[\frac{xy}{y + x}\]
\[\frac{x + y}{xy}\]
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Solution
We have to simplify `(x^-1 + y ^-1)^-1`
So,
` `(x^-1 + y ^-1)^-1 = (1/x +1/y)^-1`
= `1/ (1/x +1/y)`
`= 1/((1xx x) /(1 xx y) + (1xx x) /(1xx y))`
`= 1/(y/(xy) + x/(xy))`
`(x^-1 + y^-1)^-1 = 1/((y+x)/(xy))`
`= (xy)/(y+x)`
The value of ` (x^-1 + y ^-1)^-1` is `(xy)/(y+x)`
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