HMMT 1998 A8

Find the set of solutions for $x$ in the inequality $\frac{x+1}{x+2}>\frac{3 x+4}{2 x+9}$ when $x \neq-2, x \neq \frac{9}{2}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{-9}{2} \leq x \leq-2 \cup \frac{1-\sqrt{5}}{2}<x<\frac{1+\sqrt{5}}{2}

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