Question

What is the solution to the rational equation x over 2x plus 1 plus 1 over 4 equals 2 over 2x plus 1 ?

Answer 1

X/(2x + 1) + 1/4 = 2/(2x + 1)...multiply all terms by 2x + 1 and cancel out
x + (2x + 1)/4 = 2
3/2x + 1/4 = 2
3/2x = 2 - 1/4
3/2x = 8/4 - 1/4
3/2x = 7/4
x = 7/4 * 2/3
x = 14/12 = 7/6 <==

Answer 2

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 $\frac{x}{(2x+1)} + \frac{1}{4} = \frac{2}{(2x+1)}$.