simplifying complex fractions

[ckeenen]

Hi!

I am working on a practice problem and I know part of the answer I should arrive at but cannot figure out the steps in between. The problem is:

x is the numerator

x-x/2 is the denominator

and I am to simplify it.

I know that the denominator should be simplified to x/2 but I cannot figure out the steps to arrive at that.

Thank you so much for your help!
I am starting get very frustrated!
ckeenen

 

[soroban]

Hello, ckeenen!

Simplify: \(\displaystyle \L\:\frac{x}{x\,-\,\frac{x}{2}}\)

A complex fraction has more than two "levels".

Multiply top and bottom by the LCD of all the denominators.

In this problem, the LCD is 2.

We have: \(\displaystyle \L\:\frac{2}{2}\,\cdot\,\frac{x}{x\,-\,\frac{x}{2}} \;= \;\frac{2(x)}{2(x\,-\,\frac{x}{2})} \;=\;\frac{2x}{2x\,-\,x} \;=\;\frac{2x}{x}\;=\;2\)