Question

Select the correct option: If $x,y, 2x + \frac{y}{2}$ are nonzero real numbers, then $\bigg( 2x+ \frac{y}{2} \bigg)^{-1} \bigg \{(2x)^{-1} + \bigg( \frac{y}{2} \bigg)^{-1} \bigg\}$ equals
A. 1
B. x · y
C. x· y
D. x· y

Answer 1

Solution :

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We know the Exponential Law :

a^-n = 1/aⁿ

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Given ,

( 2x + y/2 )^-1 [ (2x)^-1 + ( y/2 )^-1 ]

= 1/( 2x + y/2 ) * [ 1/2x + 2/y ]

= 1/[ (4x+y)/2 ] * [ ( y + 4x )/( 2xy ) ]

= [ 2/( 4x + y ) ] * [ ( 2xy )/( y + 4x ) ]

After cancellation , we get

= 1/xy

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