Partial FractionsQuadratic term on the denominator

Expressions with ax2 + bx + c in the denominator decompose to terms of the form:

2

Ax B

ax bx c

2

2( 4)( 4)

x x

x x

To express

as partial fractions.

2( 4) 4

A Bx C

x x

Express as individual fractions with the factors on the denominator:

2

2

( 4) ( 4) ( 4)

( 4)( 4)

A x Bx x C x

x x

Express with a common denominator:

2

2

( ) (4 ) 4( )

( 4)( 4)

A B x B C x A C

x x

Using Method OneEquating Coefficients

Equating coefficients of x2 :

A+B = 1

Equating the coefficients of x:

-(4B-C) = 1

Equating the constant terms:

4(A-C) = 0

Using a GC or otherwise:

A = 1, B= 0, C= 1

2

2 2

1 1

( 4)( 4) ( 4) ( 4)

x x

x x x x

Hence: