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: Core 3 help

  1. Sep 16, 2007 #1

    Could someone please help me with the following question? I would really appreciate it as I am really stuck.

    Express (x + 4)/(2x^2 + 3x + 1) - 2/(2x + 1) as a single fraction in its simplest form.

    I got that [(x + 4)(2x + 1) - 2(2x^2 + 3x + 1)]/(2x^2 + 3x + 1)(2x + 1)

    = (-2x^2 + 3x + 2)/(x^2 + 3x + 1)(2x + 1) but I am not sure where to go from here.

    Thank you.

  2. jcsd
  3. Sep 16, 2007 #2


    User Avatar
    Science Advisor

    Wouldn't it make more sense to use the LEAST common denominator? Since x2+ 3x+ 1= (2x+1)(x+1) that IS a common denominator. You don't need to use the "2x+1" terrm twice. You have
    [tex]\frac{x+4}{x^2+ 3x+ 1}- \frac{2(x+1)}{x^2+ 3x+ 1}[/tex]
    That should be much simpler.

    (In your last formula, you have dropped the "2" in "2x2+ 3x+ 1".)
  4. Sep 16, 2007 #3
    Thanks so much for your help.

    I understand now.

  5. Sep 16, 2007 #4

    Could someone please help me with the following question?

    f(x) = 3 - x^2, x>= 0.

    (b) Sketch the graphs of y = f(x) and y = f^-1(x) on the same diagram.

    I got that the inverse function of f is (3 - x)^(1/2) but I do cannot figure out how to draw it in comparison to f(x). Could someone please show me.

    g(x) = 8/(3 - x), x cannot = 3.

    (e) Solve the equation f^-1(x) = g(x).

    I have no idea how to even start this last part.

    Any help would be really appreciated.

    Thank you.

  6. Sep 16, 2007 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    So, you have:


    Does that help?
  7. Sep 16, 2007 #6
    Thanks for your help.

    I have the answer now.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook