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$\lim _{x \rightarrow-}\left(\frac{x+a}{x+b}\right)^{a+b}$ is equal to
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$1$
$\lim _{x \rightarrow \infty}\left(\frac{x+a}{x+b}\right)^{a+b}=\lim _{x \rightarrow \infty}\left(\frac{1+\frac{a}{x}}{1+\frac{b}{x}}\right)^{a+b}=(1)^{a+b}=1$
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