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reciprocal of 2 consecutive integers.....

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Source: — Problem Solving |
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by DanaJ » Wed Feb 11, 2009 6:53 am
Well, you've got two consecutive integers, with x being the greatest. That means that x -1 is the other one. The reciprocals are 1/x and 1/(x - 1) respectively.
Add 1/x + 1/(x - 1) and you get (x + x - 1)/[x(x - 1)] = (2x - 1)/(x^2 - x).
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by marcusking » Wed Feb 11, 2009 7:00 am
Great job danaj, that really helped me. one question though how did you get the numerator for (x + x - 1)/[x(x - 1)] ?
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by dmateer25 » Wed Feb 11, 2009 7:05 am
marcusking wrote:Great job danaj, that really helped me. one question though how did you get the numerator for (x + x - 1)/[x(x - 1)] ?

1/x + 1/(x - 1)

Once you give these a common denominator you come up with the following:

(x-1)/x(x-1) + x/x(x-1)

Now you can combine them since they have the same denominator

(x - 1 + x) / x(x-1)

(2x-1)/(x^2-x)
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by willbeatthegmat » Wed Feb 11, 2009 7:10 am
too good...danaj..u made it look so simple....i think i just didn't understand d question...
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by marcusking » Wed Feb 11, 2009 7:15 am
thanks dmateer25, once I wrote it out on paper it became very obvious.
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