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