Question

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

Options are:
A. x = 9/2
B. x = 7/2
C. x = 3/2
D. x = 7/6

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.

Explanation:

The given equation is as follows.

`(x)/((2x+1)) + (1)/(4) = (2)/((2x+1))`

Taking L.C.D simplify the equation as follows.

`(x(4)+1(2x+1)))/(4(2x+1)) = (2)/((2x+1))`

Cancelling (2x+1) from both sides, the equation will become as follows.

`(x(4)+1(2x+1)))/(4)` = 2

4x + 2x + 1 = 8

6x + 1 = 8

6x = 7

x =
`(7)/(6)`

Thus, we can conclude that x =
`(7)/(6)` is the solution for rational equation
`(x)/((2x+1)) + (1)/(4) = (2)/((2x+1))`.