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Math Help - please help with rational expressions

  1. #1
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    please help with rational expressions

    simplify and state restrictions on the variable

    a)4x+1/3x-5 + 2x/12x-20

    b)3x-1/x^2+4x+3 - x+6/2x^2+7x+1
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  2. #2
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    Possible Solution

    a)4x+1/3x-5 + 2x/12x-20

    For this one, I would reduce second fraction by multiplying by (1/2)/(1/2), which is essentially multiplying by 1, so it is allowed:

    (4x+1)/(3x-5) + x/(6x-10)
    Now, in order to get a common denominator, we have to multiply the first fraction by 2/2 to get the lcd of 6x-10:
    (8x+2)/(6x-10) + x/(6x-10)

    Now, we can add the numerators because both fractions have the same denominator:
    (8x+2+x)/(6x-10)

    which becomes:
    (9x+2)/(6x-10)

    I don't think this could be reduced anymore.
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  3. #3
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    Additional

    Oh yeah, 6x-10 cannot equal zero because then it would cause the fraction to have a zero in the denominator.

    So, we solve 6x-10 = 0 to get:
    6x=10
    x=10/6 Reduce
    x=5/3

    So, for this problem, x cannot equal 5/3.
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