Math, asked by azkasohail01, 4 months ago

solve by partial fraction
6x³+5x²-7/3x²-2x-1

Answers

Answered by amitnrw
1

Given : 6x³+5x²-7/3x²-2x-1

To Find  : Simplify using partial fraction

Solution:

6x³+5x²-7/3x²-2x-1  

= 6x³-4x² + 9x²-2x + 2x-7/3x²-2x-1  

= 6x³-4x² - 2x  +  9x² + 2x-7 / 3x²-2x-1  

= 2x( 3x²-2x-1  ) + 9x² + 2x-7 / 3x²-2x-1  

= 2x  +   (9x² + 2x-7 / 3x²-2x-1 )

= 2x +  (9x² -6x + 6x + 2x - 3 + 3 -7 / 3x²-2x-1 )

= 2x +  (9x² -6x  - 3 + 8x- 4 / 3x²-2x-1 )

= 2x  + 3   + (8x- 4 / 3x²-2x-1 )

= 8x- 4 / 3x²-2x-1/3x²-3x+x -1  

= 8x- 4  /3x(x-1)+1(x -1)  

= 8x- 4 /(3x+1)(x-1)

8x- 4 / (3x+1)(x-1)    = A/(3x + 1)  + B/(x - 1)

=> 8x - 4 = A(x - 1)  + B(3x + 1)

x = - 1/3

=> -8/3 - 4  = A(-4/3)

=> - 8 - 12 = -4A

=> A = 5

x = 1

=> 4 = B(4)

=>  B = 1

2x  + 3   + 5/(3x + 1)  + 1/(x - 1)  

6x³+5x²-7/3x²-2x-1  = 2x  + 3   + 5/(3x + 1)  + 1/(x - 1)  

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