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

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

Subtract 2/(2x+1) from each side.

`(x)/(2x+1) - (2)/(2x+1y) - (1)/(4) = 0`

Add 1/4 to each side, and simplify the left side.

`(x-2)/(2x+1) = (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 = (9)/(2) \,\, or \,\, x = 4 (1)/(2)`