precal help
posted by Anonymous .
The numerator of a fraction is four less than the denominator The sum of the fraction and its reciprocal is 5/2 Find the numerator and denominator if each is a positive integer

denominator  x
numerator  x4
(x/x4) + (x4)/x = 5/2
times 2x(x4)
2x^2 + 2(x4)^2 = 5x(x4)
2x^2 + 2x^2  16x + 32 = 5x^2  20x
x^2 + 4x + 32 = 0
x^2 4x  32 = 0
(x8)(x+4) = 0
x = 8 or x = 4 , but x was positive
so x = 8
so original fraction was 4/8 or 1/2
check:
1/2 + 2/1 = 2 1/2 = 5/2 
the denominator of a fraction is 1 more than the numerator.the sum of the fraction and its reciprocal is 2 1/30.find the fraction