# precal help

posted by .

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 -

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

• precal help -

the denominator of a fraction is 1 more than the numerator.the sum of the fraction and its reciprocal is 2 1/30.find the fraction

## Similar Questions

1. ### Maths

When the numerator and denominator of a fraction are each increased by 5, the value of the fraction becomes 3/5 When the numerator and denominator of that same fraction are each decreased by 5, the fraction is then 1/5 Find the original …
2. ### Math

The numerator of a fraction is two less than its denominator. When both numerator and denominator are increased by 3, the fraction is incre ased by 3/20. Find the original fraction. Pls include solution and workings thx :)
3. ### Algebra

the denominator of a fractio is an integer that is one greater than the numerator. A second fraction is the reciprocal of the integer that is one less than the numerator of the first fraction. If the product of the two fraction is …
4. ### precal help

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
5. ### math

the sum of numerator and denominator is 3 less than twice the denominator.If the numerator and denominator is decreased by 1 , the numerator becomes half the denominator.Find the fraction?
6. ### Math

The numerator of a simple fraction is 2 less than its denominator. The sum of this fraction and its reciprocal is 2 4/35. Find this fraction.
7. ### algebra

The denominator of a fraction is 4 less than the numerator .If the denominator is doubled and the numerator is increased by 6,the sum of the original fraction and the new one is 3 .Find the original fraction.
8. ### basic algebra

the numerator of a certain fraction is four less then the denominator, if the numerator is doubled and the denominator is diminished by two, the sum of the original fraction and the new one is three. find the original fraction
9. ### Math

The sum of the numerator and denominator of a fraction is 3 less than twice the denomiator.If the numerator and denomiator are decreased by 1,the numerator becomes half the denominator. Determine the fraction
10. ### Math

The sum of the numerator and denominator of a fraction is 3 less than twice the denomiator.If the numerator and denomiator are decreased by 1,the numerator becomes half the denominator. Determine the fraction

More Similar Questions