Let the numerator = x

then denominator = 2x + 1

Then the fraction = \(\frac{x}{2x+1}\)

Its reciprocal = \(\frac{2x+1}{x}\)

105x^{2} + 84x + 21 = 116x^{2} + 58x

11x^{2} – 26x – 21 = 0

11x^{2} – 33x + 7x – 21 = 0

11x (x – 3) + 7 (x – 3) = 0

(x – 3) (11x + 7) = 0

⇒ x – 3 = 0 (or) 11x + 7 = 0

⇒ x = 3 (or) \(\frac{-7}{11}\)

**∴ x = 3 Numerator = 3; **

**Denominator = 2 × 3 + 1 = 7 **

**Fraction = \(\frac{3}{7}\)**