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Ranges of functions & Algebraic fractions watch

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    I'm really having problems with finding the ranges of functions and with algebraic fractions...I have posted on them before and some people explained it but when it comes to the question, I can't seem to do it.

    If someone can please tell me how to find the ranges of functions and how to add/subtract algebraic fractions by finding a common denominator.

    I know I'm asking for alot, but I've tried everything.

    Thank you...
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    Can you post some questions?
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    If someone can please tell me how to find the ranges of functions and how to add/subtract algebraic fractions by finding a common denominator.
    Don't find a common denomintor, make one.

    If you have two fractions that need adding / subtracting the denominator must be the same before you can proceed.

    This is done by simply multiplying the fractions by suitable algebraic expressions to make the denominators equal.

    When doing this you always multiply the top and the bottom of the fraction with the same expression so that you are in effect multiplying by one (so the fraction remains unchanged).

    For example:

    3/(x-1) - 12/(x-1)(x+3)

    You need to times the first fraction by (x+3)/(x+3):

    => 3(x+3)/(x-1)(x+3) - 12/(x-1)(x+3)

    Now the denominators are the same you can subtract:

    => [3(x+3) - 12]/(x-1)(x+3)

    Sometimes you need to factorise the denominators first like:

    4/(x² - 1) + 5/(6 +x)

    Where there is a difference of two squares.
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    Finding the range of a function isn't something that can be encapsulated into a magic formula. Basically the domain is the set of values you decide to put in and the range is the set of values that come out for that domain. Finding it is dependant on the function. Try sketching a graph and mark the domain on the x axis and it'll give you an idea of what the range is and how you should go about finding it.
 
 
 
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