Results 1 to 15 of 15

Math Help - Need help simplifying and solving these...

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    5

    Need help simplifying and solving these...

    I need help with these.If possible please give me a step by step guide.Thanks

    1. Simplify this: ((1-(((x^-n)+(y^-n))/((x^n)-(y^-n)))^-2) )
    2. Calculate:x=((a^2)+(a^-2)) and y=((a^3)+(a^-3)) If a+(a^-1)=5 (a not 0).
    3. (((((a^(-2x))-(a^-x)-6))/((a^(-2x))-4)) - (((a^(-x))-1)/(2-(a^(-x)))) - 2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293

    Re: Need help simplifying and solving these...

    Quote Originally Posted by loomi View Post
    I need help with these.If possible please give me a step by step guide.Thanks

    1. Simplify this: ((1-(((x^-n)+(y^-n))/((x^n)-(y^-n)))^-2) )
    2. Calculate:x=((a^2)+(a^-2)) and y=((a^3)+(a^-3)) If a+(a^-1)=5 (a not 0).
    3. (((((a^(-2x))-(a^-x)-6))/((a^(-2x))-4)) - (((a^(-x))-1)/(2-(a^(-x)))) - 2)
    Even though you have used brackets where they are needed, this is almost unreadable. A word of advice, if you have nested brackets (i.e. brackets inside brackets), the innermost brackets are round, the next set out are square, the next set out are curly, then back to round, etc...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    5

    Re: Need help simplifying and solving these...

    sorry about that
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901

    Re: Need help simplifying and solving these...

    Terribly presented.

    Is the first one:
    (\frac{{1-x^{-n}+y^{-n}}}{(x^n-y^{-n})})^{-2}

    Or is it:


    1-(\frac{{x^{-n}+y^{-n}}}{(x^n-y^{-n})})^{-2}

    Or:

    1-(\frac{{x^{-n}+y^{-n}}}{(x^n-y^{-n})^{-2}})

    Or none of the above?

    It's incredibly unclear. You've made it very difficult for anyone to help you. Please try learning latex.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2011
    Posts
    5

    Re: Need help simplifying and solving these...

    Never mind the first two here's the third one
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2011
    Posts
    5

    Re: Need help simplifying and solving these...

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member BobBali's Avatar
    Joined
    May 2010
    From
    Tanzania
    Posts
    61

    Re: Need help simplifying and solving these...

    1) \frac{\1-(x^-n)+y^-n}{(x^n)-(y^-n)^-2)} = 1 - (x^-2n) - y^-3n *using product and quotient law


    2)  X=a^2+a^-2     y=a^3 + a^-3

    Solve a+(a^-1) =5

    \frac{a^2 +1}{a} = 5a

    a^2 + 1 = 5a^2
    4a^2 = 1
    a^2 = \frac{1}{4}

    Therefore, a = \pm \frac{1}{2}
    Last edited by BobBali; November 13th 2011 at 07:38 AM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Re: Need help simplifying and solving these...

    Quote Originally Posted by loomi View Post
    Never mind the first two here's the third one
    Do you want to simplify the expression?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1

    Re: Need help simplifying and solving these...

    Quote Originally Posted by loomi View Post
    Never mind the first two here's the third one
    Let u = a^{-x}. Thus your question becomes: \dfrac{u^2 - u - 6}{u^2-4} - \dfrac{u-1}{2-u} - 2

    You can factor both the numerator and denominator the first term (perhaps something will cancel).
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901

    Re: Need help simplifying and solving these...

    a+\frac{1}{a}=5

    (a+\frac{1}{a})^2=25

    Expand and see what you get.

    Then, once you know what (a^2+\frac{1}{a^2}) is,

    Expand: (a^2+\frac{1}{a^2})(a+\frac{1}{a})
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Re: Need help simplifying and solving these...

    Quote Originally Posted by loomi View Post
    The second one: find x and y: and

    if

    x=a^2+\frac{1}{a^2}=a^2+\frac{1}{a^2}+2-2=(a+\frac{1}{a})^2-2=(5)^2-2

    y=a^3+\frac{1}{a^3}=(a+\frac{1}{a})(a^2+\frac{1}{a  ^2}-1)=(a+\frac{1}{a})(x-1)=5(22)

    EDIT: Oh! Quacky has already replied to it.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614

    Re: Need help simplifying and solving these...

    Hello, loomi!

    Here's #2 . . . basically what Quacky said.


    \text{2. If }a + a^{-1} \,=\,5\;(a \ne 0)

    . . . \text{(a) Calculate: }a^2 + a^{-2}

    We have: . . a + a^{-1} \:=\:5

    Square: . \left(a + a^{-1}\right)^2 \:=\:5^2

    n . . . . a^2 + 2 + a^{-2} \:=\:5

    . . . . . . . . a^2 + a^{-2} \:=\:3



    \text{(b) Calculate: }a^3 + a^{-3}

    We have: . . . . . a + a^{-1} \;=\;5

    \text{Cube: }\qquad\quad\;\, (a+a^{-1})^3 \;=\;5^3

    n . a^3 + 3a + 3a^{-1} + a^{-3} \;=\;125

    . . a^2 + 3\underbrace{\left(a + a^{-1}\right)}_{\text{This is 5}} + a^{-3} \;=\;125

    n . . . . . . a^3 + 15 + a^{-3} \;=\;125

    . . . . . . . . . . . a^3 + a^{-3} \;=\;110

    Follow Math Help Forum on Facebook and Google+

  13. #13
    Newbie
    Joined
    Nov 2011
    Posts
    5

    Re: Need help simplifying and solving these...

    Quote Originally Posted by Soroban View Post
    Hello, loomi!

    Here's #2 . . . basically what Quacky said.



    We have: . . a + a^{-1} \:=\:5

    Square: . \left(a + a^{-1}\right)^2 \:=\:5^2

    n . . . . a^2 + 2 + a^{-2} \:=\:5

    . . . . . . . . a^2 + a^{-2} \:=\:3


    [/size]
    Thanks but I think it was
    5^2-2=23
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901

    Re: Need help simplifying and solving these...

    I agree with you - Soroban just made a slight typo.
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Need help simplifying and solving these...

    This thread is a mess. Posts without quotes, too many questions asked and re-asked. Links that have to be clicked on to see the complete question etc. It's all over the shop. Good luck to anyone else trying to follow it.

    All members, PLEASE do NOT reply to posts that are going to create this sort of thread confusion. Report the post and let a Moderator sort things out.

    This thread is closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving and Simplifying Equations
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 5th 2009, 10:08 PM
  2. Simplifying and Solving
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 30th 2009, 07:01 PM
  3. Simplifying Fractions and Solving Trig. Equations
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: May 7th 2008, 08:06 PM
  4. Simplifying Fractions and solving for u
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 18th 2008, 12:53 PM
  5. Simplifying/Solving Trig Function
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: July 8th 2007, 04:50 PM

Search Tags


/mathhelpforum @mathhelpforum