# Thread: Help simplifying a complex fraction

1. ## Help simplifying a complex fraction

Hello,
I just started my first math class in college and its been about a year and a half since my last class in math,so Im a little rusty.
This is a function that I need to simplify to continue working the problem. I know what to do with it once its simplified I just cant remember how to do that. Here is the fraction: 2(x+3/x-2)+3 / (x+3/x-2)-1. Please explain to me how to get this fraction less complex. Thanks in advance

2. $\displaystyle \frac{2(\frac{x+3}{x-2}) + 3}{\frac{x+3}{x-2}-1}$

Is that what it looks like?

3. Yes

4. $\displaystyle \frac{2(\frac{x+3}{x-2}) + 3}{\frac{x+3}{x-2}-1}$

Find common denominator

$\displaystyle \frac{\frac{2(x+3)}{x-2} + 3}{\frac{x+3}{x-2}-1}$

$\displaystyle \frac{\frac{2(x+3) + 3x -6}{x-2}}{\frac{x+3-x+2}{x-2}}$

Cancel out the x - 2 and get

$\displaystyle \frac{2(x+3) + 3x -6}{x+3-x+2}$

You should be able to finish up from here

5. This method is longer than 11rdc11's post but it's always nice to have alternative methods:

Just substitute u back into the expression and tidy it up.