Unformatted text preview: ( xr ) ( xr )( xs ) = ( A + B ) xAsBr ( xr )( xs ) . That is, adding two fractions with constant numerator and denominators ( xr ) and ( xs ) produces a fraction with denominator ( xr )( xs ) and a polynomial of degree less than 2 for the numerator. We want to reverse this process: starting with a single fraction, we want to write it as a sum of two simpler fractions. An example should make it clear how to proceed. EXAMPLE 8.19 Evaluate Z x 3 ( x2)( x + 3) dx . We start by writing 7 x6 ( x2)( x + 3) as the sum of two fractions. We want to end up with 7 x6 ( x2)( x + 3) = A x2 + B x + 3 ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Division, Elementary arithmetic, Rational function, Divisor, Mathematics in medieval Islam, Sexagesimal

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