Answer: Option (D) is the correct answer.
Step-by-step explanation:
The given equation is as follows.
\(\frac{x}{(2x+1)} + \frac{1}{4} = \frac{2}{(2x+1)}\)
Taking L.C.D simplify the equation as follows.
\(\frac{x(4)+1(2x+1))}{4(2x+1)} = \frac{2}{(2x+1)}\)
Cancelling (2x+1) from both sides, the equation will become as follows.
\(\frac{x(4)+1(2x+1))}{4}\) = 2
4x + 2x + 1 = 8
6x + 1 = 8
6x = 7
x = \(\frac{7}{6}\)
Thus, we can conclude that x = \(\frac{7}{6}\) is the solution for rational equation \(\frac{x}{(2x+1)} + \frac{1}{4} = \frac{2}{(2x+1)}\).
