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About Alon Mandes
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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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M.A in Mathematics & Bs.c in Electronics.

You are here: Experts > Teens > Homework/Study Tips > Calculus > simplifying fractions where with x (x is to the power of -1 or less)

Calculus - simplifying fractions where with x (x is to the power of -1 or less)

Expert: Alon Mandes - 8/22/2008

Question
i have two problems i have no idea what to do on, and i realy dont know what to call them, i do know i have to simplify them.

first is:
((1/x)-(1/5))
---------------
((1/x^2)-(1/25))

and it should come out to 5x/(x+5) but i have no idea how it got there

and one more,

9-x^-2
------- (divisor)
3+x^-1

which comes to (3x-1)/x
just incase you wana know

Answer
Ok, the majour rules that we will use when simplifying is :

1. a^2-b^2=(a-b)*(a+b)

  a/b    a
2. --- = ---
   c     bc

   a     ac
3. --- = ---
  b/c    b

   a       b       ad+cd
4. --- + --- = --------
   c       d          cd

Ok, let's get to work.

1/x - 1/5          (5-x)/(5x)              (5-x)*(25x^2)
-----------    =      ----------        =     ------------    =
1/x^2 - 1/25           (25-x^2)/(25x^2)        (25-x^2)*(5x)

(5-x)*(5x)*(5x)          5x
    -------------- =      ---
   (5-x)*(5+x)*(5x)         5+x

................................................

9-x^(-2)       9 - 1/x^2        (9x^2-1)x      (3x-1)*(3x+1)*x
  ------- =    --------- = ---------    =    ------------- =
  3+x^(-1)       3 + 1/x       (3x + 1)x^2         (3x+1)*x^2

3x-1
----
x

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