1. complex rational expressions

I want to make sure that I am doing this correctly. For this expression, I rewrote the fractions with an LCD of w. I came up with

6w +3 over w - 6w over w all divided by 10w + 1 over w + 8w over w.

After combining like terms, I got 3 over w divided by 18w + 1 over w.

Did I do this correctly? If so, what is the next step?

2. $\frac{\frac{3}{w}-\frac{6}{2w+1}}{\frac{5}{w}+\frac{8}{2w+1}}=\frac{ \frac{3(2w+1)-6w}{w(2w+1)}}{\frac{5(2w+1)+8w}{w(2w+1)}}=\frac{3( 2w+1)-6w}{w(2w+1)} \times \frac{w(2w+1)}{5(2w+1)+8w}$

$=\frac{w(2w+1)(3(2w+1)-6w)}{w(2w+1)(5(2w+1)+8w)}$

$=\frac{3(2w+1)-6w}{5(2w+1)+8w}$

$\frac{3}{18w+5}$

3. Originally Posted by DivideBy0
$\frac{\frac{3}{w}-\frac{6}{2w+1}}{\frac{5}{w}+\frac{8}{2w+1}}=\frac{ \frac{3(2w+1)-6w}{w(2w+1)}}{\frac{5(2w+1)+8w}{w(2w+1)}}=\frac{3( 2w+1)-6w}{w(2w+1)} \times \frac{w(2w+1)}{5(2w+1)+8w}$
Yeaaaah I was WAY off. Why does algebra make me feel so stupid? Thank you

4. Sorry, I accidently clicked the submit button before I was finished

You can only get better at algebra with practice!

5. Originally Posted by DivideBy0
Sorry, I accidentally clicked the submit button before I was finished

You can only get better at algebra with practice!
I honestly want to be better at mathematics. Its something I have had trouble with all my life. I'm so tired of people (including teachers and tutors) who treat me like I'm an idiot just because I'm not good at math. I'm so glad I found these forums!