The given rational equation is:
[tex] \frac{x}{2x+1}-\frac{1}{4}=\frac{2}{2x+1} [/tex]
[tex] \frac{x}{2x+1}-\frac{2}{2x+1}=\frac{1}{4} [/tex]
Since the Left hand side of the equation has the same denominators,so we can subtract the numerators. So, we get
[tex] \frac{x-2}{2x+1}=\frac{1}{4} [/tex]
Cross multiplying the terms in the given equation
[tex] 4(x-2)=1(2x+1) [/tex]
[tex] 4x-8=2x+1 [/tex]
[tex] 4x-2x=9 [/tex]
[tex] 2x=9 [/tex]
[tex] x=\frac{9}{2} [/tex]
So, [tex] x=\frac{9}{2} [/tex] is the required solution to the given rational equation.
we have
[tex]\frac{x}{2x+1}-\frac{1}{4}=\frac{2}{2x+1}[/tex]
Solve for x
Multiply by [tex]4(2x+1)[/tex] both sides of the equation
[tex]4x-(2x+1)=8[/tex]
Eliminate the parenthesis
[tex]4x-2x-1=8[/tex]
Combine like terms
[tex]2x=9[/tex]
[tex]x=\frac{9}{2}[/tex]
therefore
the answer is the option A
x = 9 over 2
