Question

The denominator of a fraction is 2 more than its numerator. the reciprocal of this fraction is equal to the fraction itself. what is the sum of the numerator and denominator

Answer 1

0

Explanation:

You want the sum of numerator and denominator such that their difference is 2 and the reciprocal is equal to the original fraction.

Setup

We want a fraction such that ...

x/y = y/x

y = x +2

Solution

Substituting for y, we have ...

x/(x +2) = (x +2)/x

x^2 = x^2 +4x +4 . . . . . cross multiply

0 = 4(x +1) . . . . subtract x^2, factor

x = -1 . . . . . . . . the value of x that satisfies the equation

Then the denominator is ...

y = x +2 = (-1) +2 = 1

The sum is ...

x +y = (-1) +1 = 0

The sum of numerator and denominator is zero (0).