Decompose into partial fractions : (8x + 14) / (x + 1)(x + 5)

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We have to write (8x + 14) / (x + 1)(x + 5) as partial fractions

(8x + 14) / (x + 1)(x + 5) = A / (x +1) + B / (x + 5)

=> (8x + 14) / (x + 1)(x + 5) = A(x + 5) + B(x + 1) / (x +1)(x + 5)

=> 8x + 14 = Ax + 5A + Bx + B

=> A + B = 8 and 5A + B = 14

=> B = 8 - A

Substituting in 5A + B = 14

=> 5A + 8 - A = 14

=> 4A = 6

=> A = 6/4 = 3/2

B = 8 - 3/2 = 13/2

Therefore we have (8x + 14) / (x + 1)(x + 5) =

[3 / 2(x +1)] + [13 /...

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