Question

How do you solve `5-3/(2x-1)=(x-4)/(2x-1)` and check for extraneous solutions?

Answer 1

`x=4/9`

Explanation:

In `5-3/(2x-1)=(x-4)/(2x-1)` let us multiply each term by `(2x-1)`, assuming `2x-1!=0` or `x!=1/2`. We get

`5(2x-1)-3=x-4` or

`10x-5-3=x-4` or

`10x-x=5+3-4` or

`9x=4` or

`x=4/9`