Question 683653
The denominator of a fraction is 1 more than twice the numerator.  If 4 is added to the numerator and subtracted from the denominator, the result is the reciprocal of the fraction.  Find the original fraction.
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OF = x/(2x + 1)
(x+4)/(2x-3) = 1/OF = (2x+1)/x
(x+4)/(2x-3) = (2x+1)/x
Cross multiply
x(x+4) = (2x-3)*2x+1)
{{{x^2 + 4x = 4x^2 - 4x - 3}}}
{{{3x^2 - 8x - 3 = 0}}}
(3x + 1)*(x - 3) = 0
x = 3 --> OF = 3/7
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x = -1/3 --> OF = -1