Partial Fraction Decomposition - Problem Set

Partial Fraction Decomposition - Problem Set - Partial...

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1 Partial Fraction Decomposition- Problem Set For the following expressions (proper rational functions), find the partial fraction decompositions. 1. 2 1 1 x 2 11 1( 1 ) ( 1 ) 1 1 AB x xx x x == + −+ 1( 1 )( 1 ) Ax Bx = + ) ( ) A Bx A B =+ + + () 0 + = , 1 += 1 2 A = − , 1 2 B = 2 1 1 x 22 x x + 2. 2 3 2 +− 2 33 2( 1 ) ( 2 ) 1 2 x x x x + + + 3( 2 1 ) = ++ − 2 ) x AB + 0 + = , 23 = 1 A = , 1 B = − 2 3 2 + 12 =− + 3. 2 2 42 1 (1 ) x x + 2 1 ) 1 x xA B C x x x =+ + ++ 1 ( 1 ) ( 1 ) x x x B x C x = + + + + 1 ( ) x C x A B x B + 4 AC + = , 2 A B + = , 1 B 3 A = , 1 B = − , 1 C = 2 2 1 ) x x + + 2 31 1 1 x =− + + 4. 2 2 41 ) x + 2 ) 2 1 ( 1 ) B C x x x + + 4 1 ) ( 2 ) ) ( 2 ) x B x x C x −= + +

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2 22 41 (2 )( 222 ) x AB x ABC x A −= + + + + + 24 += , 2220 + , 1 A = − 1 A = − , 5 2 B = , 3 2 C = 2 53 1 2( 1 ) 2 1 ( 1 ) x xx x x x =− + ++ + 5. 2 23 61 (1 ) x + 2 2 2 3 ) 1 ) ) x AB C D E x x x x x + =+ + + + −− 3 2 2 2 2 6 1 ( 1) ( ( ( x Ax x B x Cx x Dx x Ex + = −+ + 2 3 2 2 2 2 2 (33 1 )(33 1 ) 1 ) ( 1 ) x A x xxx B C x D x x E x + = + + + + + 3 2 ( 3 2 3 3 3 ) x ACx AB CDx A BCDEx A BxB + = + + +− 0 AC , 32 0
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Partial Fraction Decomposition - Problem Set - Partial...

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