Posted by **Anonymous** on Friday, September 21, 2012 at 4:03am.

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

- precal help -
**Reiny**, Friday, September 21, 2012 at 8:53am
denominator --- x

numerator ---- x-4

(x/x-4) + (x-4)/x = 5/2

times 2x(x-4)

2x^2 + 2(x-4)^2 = 5x(x-4)

2x^2 + 2x^2 - 16x + 32 = 5x^2 - 20x

-x^2 + 4x + 32 = 0

x^2 -4x - 32 = 0

(x-8)(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

## Answer This Question

## Related Questions

- precal help - The numerator of a fraction is four less than the denominator The ...
- math - the sum of numerator and denominator is 3 less than twice the denominator...
- Algebra - the denominator of a fractio is an integer that is one greater than ...
- algebra - The denominator of a fraction is 4 less than the numerator .If the ...
- Math - The numerator of a simple fraction is 2 less than its denominator. The ...
- Maths - When the numerator and denominator of a fraction are each increased by 5...
- Math - The numerator of a fraction is two less than its denominator. When both ...
- algebra - The numerator of a fraction is 7 less than the denominator if three is...
- Algebra - In a certain positive fraction \frac{a}{b} , the numerator is 2 less ...
- Maths - The numerator of a fraction is 2 less than its denominator. If 3 is ...

More Related Questions