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Algebraic Fractions
Theory Refresher
Click here for "Live" theory.
An important key to the successful manipulation of algebraic fractions is knowing
how to factorise. [Go to the Factorisation refresher
now if you need to smarten your skills.]
To simplify an algebraic fraction,
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factorise the numerator and denominator;
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identify common factors between the numerator and denominator;
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divide the numerator and denominator by all the common factors (that is, cancel out common factors).
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Addition, subtraction, multiplication and division of algebraic
fractions follow the same rules presented in Arithmetic of
Fractions
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Addition and Subtraction
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Factorise the denominator of
each fraction to find the smallest common denominator. Convert the
fractions so they have this same denominator then add or subtract.
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Multiplication
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Factorise the numerator and denominator of each fraction. Write
factors of both numerators together as the new numerator, write
factors of both denominators together as the new denominator and
cancel out any common factors between the new numerator and new
denominator.
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Division
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Take the reciprocal of the second fraction and multiply.
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Important Issues.
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1.
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A fraction expresses division. Therefore, when
encountering fractions within fractions, rewrite the expression as
a division and simplify accordingly. In particular,
Alternatively, when encountering fractions within fractions,
multiply the main numerator and denominator by the denominator of
the included fraction.
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2.
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Terms that are common to both the numerator and
denominator of a fraction cannot be cancelled out. For
example, in 
the m cannot be cancelled.
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