Question

the denominator of a fraction is 2 more than its numerator if the sum of the fraction and its reciprocal is 34by15 find the fraction

Answer 1

the denominator of a fraction is 2 more than the numerator. the sum of the fraction and its reciprocal is 34/15. find the fraction.

:

Let x = the numerator, then (x+2) = the denominator

: x/(x+2) + x+2/x= 34/15:

Multiply equation by 15x(x+2) and you have:

15x(x) + 15(x+2)(x+2) = 34x(x+2)

:

15x^2 + 15(x^2 + 4x + 4) = 34x^2 + 68x

:

15x^2 + 15x^2 + 60x + 60 = 34x^2 + 68x

:

30x^2 + 60x + 60 = 34x^2 + 68x

:

0 = 34x^2 - 30x^2 - 60x + 68x - 60

:

0 = 4x^2 + 8x - 60

:

Simplify, divide by 4

x^2 + 2x - 15 = 0

:

Factors to:

(x + 5)(x - 3) = 0

:

x = -5: the fraction is 5/3

and

x = + 3; the fraction is 3/5

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