Question

Need answer to question 19 please !!

Answer 1

(1/3) / (x+1) + (-1/3) / (x+4)

Explanation:

1 / (x+1)(x+4) = (A/x+1) + (B/x+4)

1 = ((A/x+1) + (B/x+4)) * (x+1)(x+4)

1 = A*(x+4) + B*(x+1)

* if x = -4

1 = A*(-4+4) + B*(-4+1)

1 = B*(-3)

B = -1/3

** if x = -1

1 = A*(-1+4) + B*(-1+1)

1 = A*(3)

A = 1/3

check: (1/3)/(x+1) + (-1/3)/(x+4) = ((1/3)*(x+4))/((x+1)(x+4)) + ((-1/3)*(x+1))/((x+1)(x+4))

==> ((1/3x + 4/3)+(-1/3x - 1/3)) / ((x+1)(x+4)) = 1 / (x+1)(x+4)