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