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Unformatted text preview: The Empire Builder, 1957 6.5 day 1 Partial Fractions Greg Kelly, Hanford High School, Richland, Washington 2 5 3 2 3 x dx x xâˆ« This would be a lot easier if we could rewrite it as two separate terms. ( 29 ( 29 5 3 3 1 x x x+ 3 1 A B x x = ++ 1 â†’ These are called nonrepeating linear factors. You may already know a shortcut for this type of problem. We will get to that in a few minutes. 2 5 3 2 3 x dx x xâˆ« This would be a lot easier if we could rewrite it as two separate terms. ( 29 ( 29 5 3 3 1 x x x+ 3 1 A B x x = ++ Multiply by the common denominator. ( 29 ( 29 5 3 1 3 x A x B x = + +5 3 3 x Ax A Bx B = + +â‹… Set liketerms equal to each other. 5 x Ax Bx = + 3 3 A B =â‹… 5 A B = + 3 3 A B =Solve two equations with two unknowns. 1 â†’ 2 5 3 2 3 x dx x xâˆ« ( 29 ( 29 5 3 3 1 x x x+ 3 1 A B x x = ++ ( 29 ( 29 5 3 1 3 x A x B x = + +5 3 3 x Ax A Bx B = + +â‹… 5 x Ax Bx = + 3 3 A B =â‹… 5 A B = + 3 3 A B =Solve two equations with two unknowns....
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 Spring '08
 Smith
 Division, Fractions, Elementary arithmetic, ax

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