We want to solve
[tex] \frac{x}{2x+1} - \frac{1}{4} = \frac{2}{2x+1} [/tex]
Subtract 2/(2x+1) from each side.
[tex] \frac{x}{2x+1} - \frac{2}{2x+1y} - \frac{1}{4} = 0[/tex]
Add 1/4 to each side, and simplify the left side.
[tex] \frac{x-2}{2x+1} = \frac{1}{4} [/tex]
Cross multiply.
4(x - 2) = 1(2x + 1)
4x - 8 = 2x + 1
Simplify and solve for x.
4x - 2x = 1 + 8
2x = 9
x = 9/2 or x = 4 1/2.
Answer: [tex]x = \frac{9}{2} \,\, or \,\, x = 4 \frac{1}{2} [/tex]
