Algebra: Partial Fractions

Worked Solution:

The denominator is of degree 2 so we will need 2 partial fractions :

24 v + 13 ( v – 5 )( 3 v + 4 )

=

a v – 5

+

b 3 v + 4

Multiplying both sides by ( v – 5 )( 3 v + 4 )

24 v + 13

= a(

3 v + 4

)

+ b

(v – 5)

This is an identity: it must be true for all values of v:
To make (v – 5) zero, let v = 5:

133 = 19 a
a = 7

To make (3 v + 4) zero, let v = –4/3:

–19 = –19/3 b
b = 3