# Solving Rational Equations

1. Oct 13, 2011

### anonymous12

1. The problem statement, all variables and given/known data

In the picture above, I solved the rational equation using two different methods. In the first method I got x = 1 and in the second method I got x = 4/3. Which answer is correct or are both of them incorrect? Thanks.

2. Oct 13, 2011

### Staff: Mentor

If you're going to do your work on paper, and then take a picture of it and upload it, at least do us the courtesy of
1) providing a reasonably decent picture
2) providing a picture that is oriented the right way

3. Oct 13, 2011

### SammyS

Staff Emeritus
The rational equation is:
$\displaystyle \frac{3}{x+2}-\frac{1}{x}=\frac{1}{5x}\,.$​

It's easy to check by plugging in the answers.

Never mind. You do show your work in a hard to read sideways image.

The first method is wrong because you failed to multiply the right side by x(x+2). You must multiply BOTH SIDES of the equation by the same thing.

The second method was OK. You multiplied both sides by an extra x, which gave you an extraneous solution. x=4/3 is correct.

Last edited: Oct 13, 2011
4. Oct 13, 2011

### anonymous12

EDIT: Yup, 4/3 is the correct answer. Thanks for the help.