SOLUTION: the denominator of a positive fraction is one more than twice the numerator .if the sum of the fraction and its reciprocal is 2.9;find the fraction

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Question 881045: the denominator of a positive fraction is one more than twice the numerator .if the sum of the fraction and its reciprocal is 2.9;find the fraction
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The fraction is
X%2F%281%2B2X%29
.
.
.
X%2F%281%2B2X%29%2B%281%2B2X%29%2FX=2.9
X%5E2%2B%281%2B2X%29%5E2=2.9X%281%2B2X%29
10%28X%5E2%2B1%2B4X%2B4X%5E2%29=29X%2B58X%5E2
10%285X%5E2%2B4X%2B1%29=58X%5E2%2B29X
50X%5E2%2B40X%2B10=58X%5E2%2B29X
8X%5E2-11X-10=0
%288X%2B5%29%28X-2%29=0
Only the integer solution makes sense in this case,
X-2=0
X=2
Verifying the solution,
2%2F%281%2B2%282%29%29=2%2F5
2%2F5%2B5%2F2=4%2F10%2B25%2F10=29%2F10=2.9