Challenge: find an approximation for Result = (47-X)/X

I'm looking for an approximation of the simple formula:

Result = (47-X)/X

For X = 1; result = 46
For X = 2; result = 22.5
For X = 3; result = 14.6
For X = 4; result = 10.75
For X = 5; result = 8.4
For X = 6; result = 6.8

I'd like to find an approximation that is easy and fast to calculate on the fly, it doesn't have to be accurate, the big ballpark is close enough.

Any idea is welcome and I do mean 'any'.

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The thing I am mainly looking for is:
I'd like a memory support for the results with x = 1 to 20

So either some sort of mnemonic, an approximated formula, anything that can help me remember this sequence of results:

result = 46
result = 22.5
result = 14.6
result = 10.75
result = 8.4
result = 6.8
.
.
.

Thanks in advance,
Andy

Re: Challenge: find an approximation

(47 - x) / x
= 47/x - x/x
= 47/x - 1
Methinks you can't simplify it any further...