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Question:

vennetti
vennetti
Student
High School - 11th Grade

(5x+3/x)-(x-1/2x)

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Posted by vennetti on Sunday March 1, 2009 at 6:46 PM and tagged with math, simplest form.

Answers:


  1. kmieciakp Teacher
    High School - 12th Grade

    Either:

    [(5x+3)/x] - [(x-1) / 2x] 

    adjust with common denominator, 2x:

    (10x + 6)/2x - [(x-1)/2x]

    distribute the negative:

    10x + 6/2x + [(-x+1)/2x]

    solve:

    10x +6/2x + (1-x)/2x

    10x + 6 +1 -x /2x

    9x +7 /2x

    4.5 + 3.5x

    --------------------------------

    OR

    [(5x) +3/x] - [(x)-1/2x)]

    distribute the negative:

    5x +3/x + (-x) + 1/2x

    common denominator 2x:

    10x^2/2x +6/2x + (-2x^2)/2x + 1/2x

    solve:

    [10x^2 + 6 + (-2x^2) + 1] / 2x

    (8x^2 + 7) / 2x

    (8x^2 /2x ) + 7/2x

    4x + 3.5x

    x(4+3.5)

    7.5x

     

     

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    Posted by kmieciakp on Sunday March 1, 2009 at 7:40 PM

  2. neela
    neela Teacher
    Graduate School

    eNotes Editor

    (5x+3/x)-(x-1/2x) :

    In mathematics the first bracket is only decorative.

    (5x+3/x) =5x+(3/x). And cannot mean (5x+3)/x.

    -(x-1/2x) = -x+(1/2)x, and cannot mean (x-1)/(2x). 1/2x is not 1/(2x) but it means (1/2)x.

     

    Therefore

    5x+(3/x)-x+(1/2)x =5x-x+(1/2)x+(3/x)

    =(5-1+0.5)x+3/x = 4.5x+3/x

    *---*--------*-----------*

    If you wanted the factors:The expression is equal to  (1/x)(4.5x^2 +3)  or  (2/x)(9x^2 +6) .

    If you wanted to solve for zeros:

    No real solution and Y axis is an asymptote.

    y=4.5x is another obleque asynptote.

    The expression is discontinuous at x= 0 with an infinite jump from positive infinity to negative infinity as x change sign around zero i.e from  0+  to  0- .

     

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    Posted by neela on Thursday June 11, 2009 at 7:54 AM

  3. popocatepetl
    popocatepetl Teacher
    Graduate School

    multiply top and bottom of the 1st fraction by 2 to match denominators & get

    (10x + 6) /2x   now rewrite the numberator to match the numerator of the second fraction so that you get

    ( 9x+x-1+7 ) /2x  - ( x-1 )/2x )

    Now write the difference of the numerators over 2x to get

    ( 9x+7 ) / 2x

     

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    Posted by popocatepetl on Thursday October 22, 2009 at 9:19 PM