Question

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

A. x = 9 over 2
B. x = 7 over 2
C. x = 2
D. x = 3

Answer 1

The given rational equation is:

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

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

Since the Left hand side of the equation has the same denominators,so we can subtract the numerators. So, we get

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

Cross multiplying the terms in the given equation

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

`4x-8=2x+1`

`4x-2x=9`

`2x=9`

`x=(9)/(2)`

So,
`x=(9)/(2)` is the required solution to the given rational equation.

Answer 2

we have

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

Solve for x

Multiply by
`4(2x+1)` both sides of the equation

`4x-(2x+1)=8`

Eliminate the parenthesis

`4x-2x-1=8`

Combine like terms

`2x=9`

`x=(9)/(2)`

therefore

the answer is the option A

x = 9 over 2