The numerator of a fraction is three less than the denominator. The sum of the fraction and four times its reciprocal is 17/2. How do you find the fraction?

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Answer 1 · 2016-06-02T14:00:22

Let the numerator be x.

#x/(x + 3) + 4 xx (x + 3)/x = 17/2#

#x/(x + 3) + (4x + 12)/x = 17/2#

Put on a common denominator.

#(x^2 + (4x + 12)(x + 3))/((x)(x + 3)) = 17/2#

#(x^2 + 4x^2 + 12x + 12x + 36)/((x)(x + 3)) = 17/2#

#2(5x^2 + 24x + 36) = 17(x^2 + 3x)#

#10x^2 + 48x + 72 = 17x^2 + 51x#

#0 = 7x^2 + 3x - 72#

#0 = 7x^2 - 21x + 24x - 72#

#0 = 7x(x - 3) + 24(x - 3)#

#0 = (7x + 24)(x - 3)#

#x = -24/7 and 3#

The fraction is #3/6 = 1/2# or #8/1 = 8#

Hopefully this helps.