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Calc06_5day1

# Calc06_5day1 - The Empire Builder 1957 6.5 day 1 Partial...

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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 x---âˆ« This would be a lot easier if we could re-write 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 non-repeating linear factors. You may already know a short-cut for this type of problem. We will get to that in a few minutes. 2 5 3 2 3 x dx x x---âˆ« This would be a lot easier if we could re-write 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 like-terms 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 x---âˆ« ( 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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Calc06_5day1 - The Empire Builder 1957 6.5 day 1 Partial...

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