Question

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

Answer 1

$\dfrac{x}{2x-1}-\dfrac{1}{4}=\dfrac{2}{2x-1}\ \ \ |add\ \dfrac{1}{4}\ to\ both\ sides\\\\\dfrac{x}{2x-1}=\dfrac{2}{2x-1}+\dfrac{1}{4}\ \ \ |subtract\ \dfrac{2}{2x-1}\ from\ both\ sides\\\\\dfrac{x}{2x-1}-\dfrac{2}{2x-1}=\dfrac{1}{4}\\\\\dfrac{x-2}{2x-1}=\dfrac{1}{4}\ \ \ \ |cross\ multiply\\\\4(x-2)=1(2x-1)\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\(4)(x)-(4)(2)=(1)(2x)-(1)(1)\\\\4x-8=2x-1\ \ \ \ |add\ 8\ to\ both\ sides\\\\4x=2x+7\ \ \ |subtract\ 2x\ from\ both\ sides$

$2x=7\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\huge\boxed{x=\frac{7}{2}}\leftarrow\boxed{b.}$