Question

The denominator of a fraction is 1 more than twice its numerator. If the sum of the fraction and its reciprocal is 34/15. Find the fraction.
(Class 10 Maths Sample Question Paper)

Answer 1

Solution:
Let's numerator be x.

Denominator is x+2.

Fraction= numerator /denominator

Fraction= x/(x+2)

A.T.Q

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

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

x² + x² +4x +4 = (34/15)(x²+2x)

15(2x² + 4x +4 ) = 34(x²+2x)

30x² + 60x + 60 = 34x² + 68x

34x² - 30x² + 68x-60x -60= 0

4x² + 8x -60 = 0

4(x² +2x -15)= 0

x² +2x -15 = 0

x² +5x -3x -15= 0

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

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

x-3= 0

x= 3

x+5=0

x= - 5    (not possible)

Fraction=  x/(x+2) = 3 /(3+2)= ⅗

Hence,the Fraction= ⅗

HOPE THIS WILL HELP YOU...