SOLUTION: (x/(x+2))+((x-4)/(2x))=((x-2)/x) I've been told that x equals only 2. the best I've done is x equals 2 or 0. please help! where am i going wrong?

Algebra ->  Rational-functions -> SOLUTION: (x/(x+2))+((x-4)/(2x))=((x-2)/x) I've been told that x equals only 2. the best I've done is x equals 2 or 0. please help! where am i going wrong?      Log On


   

Question 745428: (x/(x+2))+((x-4)/(2x))=((x-2)/x)
I've been told that x equals only 2. the best I've done is x equals 2 or 0.
please help! where am i going wrong?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
By only reading but not actually solving your exercise problem, what you may have done was to find two solutions: one of them a correct result and the other an extraneous result. That may sometimes happen when you have rational equations to solve. You need to check how your resulting solutions work IN THE ORIGINAL EQUATION to find if they work or not work.

You can be sure that x=0 WILL NOT WORK in the original equation because you would be writing a part of the expression giving division by zero, and this is an impossibility. Particularly, 2*0 cannot be a divisor, and 0 cannot be a divisor. You can NOT let x=0.