1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simplify an expression

  1. Dec 9, 2017 #1
    1. The problem statement, all variables and given/known data
    I have to prove that the expression

    $$\frac{\omega C - \frac{1}{\omega L}}{\omega C - \frac{1}{\omega L} + \omega L - \frac{1}{\omega C}}$$

    is equal to

    $$\frac{1}{3-( (\frac{\omega_r}{\omega})^2 + (\frac{\omega}{\omega_r})^2)}$$

    where ##\omega_r= \frac{1}{\sqrt{LC}}##

    2. Relevant equations
    3. The attempt at a solution

    What I started to do was to get rid of the denominators in the fraction and put everything together


    Then I divided the denominator by the numerator


    And I'm kind of stuck now. Can someone give an hint on how should I proceed next?
    Or is there any easier way to start the proof? I'm just looking for a hint, thanks.
    Last edited by a moderator: Dec 9, 2017
  2. jcsd
  3. Dec 9, 2017 #2


    User Avatar
    Science Advisor
    Homework Helper

    You could start by checking for a typo in the expressions you gave. If you put ##L=C=1## you can easily see that they aren't equal.
  4. Dec 9, 2017 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    First of all, get rid of L and C in favour of ##\omega_r## as soon as possible. It will save you a lot of writing and make your goal clearer. Second, your desired expression has a 3 in the denominator and you have a 1. How can you compensate for this?

    I also suggest working with the reciprocal of your expression. It will save you having to write the expression as a quotient.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted