Find the partial fraction decomposition of the rational function <mstyle displaystyle="true" scr

Janiyah Huffman

Janiyah Huffman

Answered question

2022-05-21

Find the partial fraction decomposition of the rational function 2 x 3 + 7 x + 5 ( x 2 + x + 2 ) ( x 2 + 1 )
I have tried dividing first but keep running into problem after problem.

Answer & Explanation

Carter Escobar

Carter Escobar

Beginner2022-05-22Added 9 answers

Try writing your fraction as a sum of A 0 + A 1 x x 2 + 1 + B 0 + B 1 x x 2 + x + 2 and then find A 0 , A 1 and B 0 , B 1 by equating ( A 0 + A 1 x ) ( x 2 + x + 2 ) + ( B 0 + B 1 x ) ( x 2 + 1 ) = 2 x 3 + 7 x + 5
The final answer should be
2 x 3 + 7 x + 5 ( x 2 + x + 2 ) ( x 2 + 1 ) = 5 x 2 + 1 + 2 x 5 2 + x + x 2

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