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Algebraic Methods (algebraic fractions (partial farctions (meathods (put…
Algebraic Methods
algebraic fractions
algebraic fractions work in the same way as numeric fractions. you can simplify them by cancelling common factors and finding common denominators
to multiply fractions cancel any common factors then multiply the numerators and multiply the denominators
to add or subtract two fractions find a common denominator (usually the product of the denominators)
to divide fractions cancel any common factors then multiply the first by the reciprocal of the second
partial farctions
a single fraction with two or more distinct linear factors in the denominator can be split into two or more separate fractions with linear denominators
meathods
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substitution
choose values of x that eliminate all but one of A,B or C
repeated factors- a single fraction with a repeated linear factor in the denominator can also be slit into partial fractions, remember to have all orders of the repeated factor
Proof by contradiction
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To prove a statement by contradiction you start by assuming that it is not true. you then use logical steps to show that this assumption leads to something impossible ( either a contradiction of the assumption or a contradiction of a fact you know to be true( eg: 2+3=3). you then conclude that your assumption was incorrect and that the original statement was true
important assumptions
a rational number can be written as A/B where a and b are integers and the fraction is in its lowest form
a irrational number cannot be written as A/B where a and b are integers and the fraction is in its lowest form
algebraic division
an improper algebraic fraction is one whose numerator has a degree equal to or larger than the denominator. an improper fraction must be converted to a mixed fraction before you can express it in partial fractions
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