Question

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

Answer 1

We want to solve
$\frac{x}{2x+1} - \frac{1}{4} = \frac{2}{2x+1}$

Subtract 2/(2x+1) from each side.
$\frac{x}{2x+1} - \frac{2}{2x+1y} - \frac{1}{4} = 0$

Add 1/4 to each side, and simplify the left side.
$\frac{x-2}{2x+1} = \frac{1}{4}$

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:  $x = \frac{9}{2} \,\, or \,\, x = 4 \frac{1}{2}$