IS. 2 Given that $x$ is a negative real number that satisfy $\frac{1}{x+\frac{1}{x+2}}=a$. If $b=x+\frac{7}{2}$, find the value of $b$
$\frac{1}{x+\frac{1}{x+2}}=2 \Rightarrow \frac{x+2}{x(x+2)+1}=2 \Rightarrow x+2=2 x^{2}+4 x+2 \Rightarrow 2 x^{2}+3 x=0 \Rightarrow x=-1.5$ or 0 (reject)
$$
b=-1.5+3.5=2
$$