Question

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

Answer 1

Let the numerator of the fraction be x.

Then the denominator of the fraction will be 1 more than twice its denominator = 2x + 1.

Therefore the resultant fraction = x/2x + 1.  ----- (1)

Given that sum of the fraction and its reciprocal is 34/15.

$\frac{x}{2x + 1} + \frac{2x + 1}{x} = \frac{34}{15}$

$\frac{x^2 + (2x+1)^2}{x(2x+1)} = \frac{34}{15}$

$\frac{x^2 + (4x^2 + 4x + 1)}{2x^2 + x} = 34/15$

$\frac{x^2 + 4x^2 + 4x + 1}{2x^2 + x} = \frac{34}{15}$

$15(5x^2 + 4x + 1) = 34(2x^2 + x)$

75x^2 + 60x + 15 = 68x^2 + 34x 

75x^2 + 26x + 15 = 68x^2

7x^2 + 26x + 15 = 0

7x^2 + 21x + 5x + 15 = 0

7x(x + 3) + 5(x + 3) = 0

(7x + 5) = 0 (or) x + 3 = 0

x = -5/7 (or) x = -3.  ----- (2)


Substitute (2) in (1), we get

The fraction = -3/2(-3) + 1

                     = -3/-6 + 1

                    = 3/5.


The reciprocal fraction = 5/3.

Answer 2

Answer:

5/3 huuuuuu buuuuuu suuuuu duuuuu