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

n = d  4
[(d  4) / d] + [d / (d  4)] = 5/2
multiplying by [2 * d * (d  4)]
[2 (d  4)^2] + (2 d^2) = 5 d (d  4)
2d^2  16d + 32 + 2d^2 = 5d^2  20d
0 = d^2  4d  32
factoring __ 0 = (d  8)(d + 4)
0 = d  8 __ 8 = d