Answer:
a)
Step-by-step explanation:
[tex]\dfrac{3p-1}{p^2-1}[/tex]
Factorize the denominator:
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}[/tex]
Therefore,
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}=\dfrac{A}{p+1}+\dfrac{B}{p-1}[/tex]
[tex]\implies 3p-1=A(p-1)}+B(p+1)[/tex]
When p = 1:
[tex]\implies 2=A(0)}+B(2)[/tex]
[tex]\implies B=1[/tex]
When p = -1:
[tex]\implies -4=A(-2)}+B(0)[/tex]
[tex]\implies A=2[/tex]
Therefore,
[tex]\implies \dfrac{3p-1}{(p+1)(p-1)}=\dfrac{2}{p+1}+\dfrac{1}{p-1}[/tex]
