(Q7)The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocol is 2
16
21
find the fraction.

Answer:

Let the numerator = x

Then denominator = 2x + 1

Then the fraction
x
2x + 1

Its reciprocal=
2x + 1
x

By problem
x
2x + 1
+
2x + 1
x
= 2
16
21

x2+(2x + 1)2
(2x + 1)x
=
58
21

x2 +4x2 +4x +1
2x2 +x
=
58
21

105x2 +84x +21 = 116x2 +58x

11x2 -26x -21 = 0

11x2 - x + 7x - 21 = 0

11x(x - ) + 7(x - ) = 0

(x - x)(11x + 7) = 0

x - x = 0 or 11x + 7 = 0

x = x or
-7
11

x = x

Numerator =

Denominator = 2 × x + 1 =

Fraction =