# Rational Function

Algebra Level 4

Consider the function $$f(x)=\dfrac{x^{2}+ax+b}{x^{2}+2x+3}$$ where $$a$$ and $$b$$ are positive integers.

If the range of $$f(x)$$ is $$[-5,4],$$ find the value of $$a^{2}+b^{2}-ab.$$

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