Question

[4x -1/

(x+4) (4x² +1)]=
[A\
x+ 4]+
[Bx+C\
4x² + 1]
after clearing fractions to decompose, the equation 4x - 1 =A(4x^2+1) + (BX+C)(x + 4) results. If x= -4 what is the value of A?

Answer 1

A = -
`$ (17)/(65) $`

Explanation:

Given: 4x - 1 = A[4x² + 1] + (Bx + c)(x + 4)

To determine the value of A, we have to eliminate the other two variables, viz, B and C.

To do this simply put x = -4.

We get:

4(-4) - 1 = A[4(-4)² + 1] + 0

⇒ -17 = A(65)

∴ A =
`$ (17)/(65) $` is the answer.