Question

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

a. x=2
b. x= 7/2
c. x=3
d. x=7/6

Answer 1

`(x)/(2x-1)-(1)/(4)=(2)/(2x-1)\ \ \ |add\ (1)/(4)\ to\ both\ sides\\\\(x)/(2x-1)=(2)/(2x-1)+(1)/(4)\ \ \ |subtract\ (2)/(2x-1)\ from\ both\ sides\\\\(x)/(2x-1)-(2)/(2x-1)=(1)/(4)\\\\(x-2)/(2x-1)=(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=(7)/(2)}\leftarrow\boxed{b.}`