Question

Decompose 3p-1/p^2-1 into partial functions

(please select from the choices)

Answer 1

a)

Explanation:

`(3p-1)/(p^2-1)`

Factorize the denominator:

`\implies (3p-1)/((p+1)(p-1))`

Therefore,

`\implies (3p-1)/((p+1)(p-1))=(A)/(p+1)+(B)/(p-1)`

`\implies 3p-1=A(p-1)}+B(p+1)`

When p = 1:

`\implies 2=A(0)}+B(2)`

`\implies B=1`

When p = -1:

`\implies -4=A(-2)}+B(0)`

`\implies A=2`

Therefore,

`\implies (3p-1)/((p+1)(p-1))=(2)/(p+1)+(1)/(p-1)`