Question 33·Hard·Equivalent Expressions

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Suppose

\frac{x^3 + ax^2 + bx + c}{x^2 + 3x + 2} = x + 4 + \frac{5}{x^2 + 3x + 2}

for all real values of $x$ such that the denominator is nonzero, where $a$ , $b$ , and $c$ are constants. What is the value of $b$ ?

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