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# C1notes - Supplementary Course Module C Rational...

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Supplementary Course Module C: Rational Expressions Assignment 1 ° Simplifying Rational Expressions Factoring: ° A rational expression may be able to be simpli°ed if the numerator and denominator can be expressed as a product of factors. Any factor that is common to both the numerator and denominator can be cancelled (similar to how we ±reduced² fractions: 15 20 = 3 ° 5 4 ° 5 = 3 4 ). ° When we cancel, we are, in effect, dividing both the numerator and the denominator by the same factor ( i.e., we can also think of 15 20 = 15 ± 5 20 ± 5 = 3 4 ). ° If the factor is an algebraic expression, we have to be careful that we are not dividing by a value equal to zero ³ recall that division by zero is not allowed! ° a b = ac bc , c 6 = 0 and ad bd = a b , d 6 = 0 ° any possible values which would result in division by zero are stated as restrictions, exempli°ed by the following. examples: x 2 + x ± 12 x 2 ± 4 x + 3 = ( x + 4) ( x ± 3) ( x ± 1) ( x ± 3) = x + 4 x ± 1 , provided x 6 = 3 12 x 2 y ± 9 x 3 y 4 + 3 x 2 y 2 3 x 2 y 2 = 3 x 2 y ° 4 ± 3 xy 3 + y

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C1notes - Supplementary Course Module C Rational...

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