Question

Solve the following for x: 2x over x+1=1/3-2 over x-1 ( Solve for x, than check your answer is it extraneous)?

Answer 1

\[{2x \over x+1}={{1\over3}-2\over x-1}\]or\[{2x \over x+1}={1\over3}-{2\over x-1}\]???

Answer 2

The second one is correct besides the last problem should be instead of 2 over x-1 it should be 2 over x+1

Answer 3

well that makes it much easier\[{2x \over x+1}={1\over3}-{2\over x+1}\]multiply it all by x+1:\[2x={(x+1)\over3}-2={x \over3}+{1\over3}-2={x \over3}-{5\over3}\]combine like terms:

Answer 4

\[2x-{x \over3}={5x \over3}=-{5\over3}\]multiply both sides by 3/5:\[x=-1\]