Which Method is Correct for Solving Rational Equations?

[anonymous12]

Homework Statement

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.

 

[Mark44]

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

 

[SammyS]

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.

[STRIKE]Explain in more detail how you arrived at those answers so we can help you.[/STRIKE]

Added in edit:

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.

 

[anonymous12]

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