One half of a number decreased by its reciprocal

5

Step-by-step explanation:

Let the number equal x. Half the number is then  

x

2

and the reciprocal of that is  

2

x

The reciprocal of the number is  

1

x

and half that is  

1

2

x

then  

2

x

+

1

2

x

=

1

2

4

x

+

x

2

x

2

=

1

2

10

x

=

2

x

2

2

x

2

−

10

x

=

0

2

x

(

x

−

5

)

=

0

Zero is not viable solution as its reciprocal is infinity. The answer is therefore  

x

=

5