A function \(f(x)=\frac{Ax^3+Bx^2+Cx+D}{x^2+x-2}\) satisfies both \(\displaystyle \lim_{x \to 1} f(x)=2\) and \(\displaystyle \lim_{x \to \infty} f(x)=1\). What is the value of \(f(4)?\)

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