# Thread: [SOLVED] Simplifying complex rational expressions

1. ## [SOLVED] Simplifying complex rational expressions

Hi,

I need help with the problem below and would really appreciate an explanation as to how each step is done.

Thank you!

x - 1
4
___________
x-4

(x over 4 minus 1 divided by x minus 4)

2. $
\frac{\displaystyle\frac{x}{4}-1}{x-4}
$

That looks disgusting to work with. First, I'm just going to rewrite the top as a whole fraction:

$
=\frac{\displaystyle\frac{x-4}{4}}{x-4}
$

Now, this could be written as:

$
=\frac{x-4}{4} \div (x-4)
$

Can you see how that would equal $\frac {1}{4}$? If not, I'll try to explain further.

3. Yes, that helped a lot and I understand how you got 1/4. Thank you much!