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Math Help - Dividing out a variable from a quotient

  1. #1
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    Dividing out a variable from a quotient

    I don't think I've ever mastered this concept. If I have a problem like  \frac{x+2a+3b}{x} = {4} , can I just divide the x out to get  1+2a+3b = 4 ?

    I know if I look at the first expression like  \frac{x}{x} + \frac{2a}{x} + \frac{3b}{x} then I could turn x/x into 1, but the expression would look like  1 + \frac{2a}{x} + \frac{3b}{x} . The x could get brought back into the quotient if it had a common denominator.

    Also, if the sample problem were  \frac{x*2b+a}{x} would that make a difference in mathematical rules for dividing out the x? (As opposed to addition or subtraction).

    I hope my question makes sense, if not I can explain more.
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  2. #2
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    Re: Dividing out a variable from a quotient

    Quote Originally Posted by AZach View Post
    I don't think I've ever mastered this concept. If I have a problem like  \frac{x+2a+3b}{x} = {4} , can I just divide the x out to get  1+2a+3b = 4 ?
    No. x is not a factor of the top; you cannot simply cancel out the x.

    The correct simplification is 1 + \frac{2a}{x} + \frac{3b}{x} = 4, as you did, or alternatively, 1 + \frac{2a+3b}{x} = 4.
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