# Rational Connection!

Algebra Level 4

$\large f(x)=\frac{ax^2+6x+b}{x^2-1} \:\:\text{and} \:\:\large g(x)=\frac{(a+b)x^2+60x-54}{x^2-1}$

Let $$f(x)$$ and $$g(x)$$ be defined by the given formulas on the set $$\mathbb{R}-\{-1, 1\}.$$ If the range of $$f(x)$$ is the set $$\mathbb{R}$$, then which one of the following is the range of $$g(x).$$

Inspiration

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