Question

When simplified \[( x^{- 1} + y^{- 1} )^{- 1}\] is equal to

पर्याय

• xy

• x+y

• \[\frac{xy}{y + x}\]

• \[\frac{x + y}{xy}\]

Answer 1

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)`