Decompose into partial fractions Decompose into partial frac

Decompose into partial fractions

Decompose into partial fractions 10x + 2/4x^2 + 4x + 1 -5x^2 + 6x - 2/x^3 + 27 4x^4 - 2x^3 + 22x^2 - 6x + 48/x (x^2 + 4)^2

52. (10x + 2)/(4x^2 + 4x + 1) = (10x+2)/(2x+1)^2

(10x+2)/(2x+1)^2 = A1/(2x+1) + A2/(2x+1)^2

=> (10x+2) = A1(2x+1) + A2

(10x+2) = 2A1.x + A1 + A2

Comparing the terms,

2A1 = 10 => A1 = 5

and A1 + A2 = 2

A2 = 2 - 5 = -3

Hence (10x + 2)/(4x^2 + 4x + 1) = 5/(2x+1) - 3/(2x+1)^2

$Decompose into partial fractions Decompose into partial fractions 10x + 2/4x^2 + 4x + 1 -5x^2 + 6x - 2/x^3 + 27 4x^4 - 2x^3 + 22x^2 - 6x + 48/x (x^2 + 4)^2Solut$

Decompose into partial fractions Decompose into partial frac

Solution

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