Casella and Berger 2002 Statistical Inference p71

Question

I wonder if this is a mistake on P71 of Casella and Berger (2002), Statistical Inference. When they define the function $g(x,\lambda)$, they have $$ g(x,\lambda) = \frac{x^n e^{-x/(\lambda+\delta_{0})}}{(\lambda-\delta_{0})^2} \left(\frac{x}{\lambda-\delta_{0}}+1 \right). $$ But, shouldn't the power of the exponet be $-x/(\lambda-\delta_{0})$ instead of having a plus sign in front of $\delta_{0}$? This function $g$ is designed to be larger than $$ \frac{x^ne^{-x/\lambda}}{\lambda^2} \left( \frac{x}{\lambda}+1 \right). $$ For some constant $\delta_{0}$ satifying $0<\delta_{0}<\lambda$ and $x>0$, $$ \frac{x}{\lambda}+1\leq \frac{x}{\lambda-\delta_{0}}+1 $$ and $$ \frac{x^n}{\lambda^2}\leq \frac{x^n }{(\lambda-\delta_{0})^2} $$ but $$ e^{-x/\lambda} \geq e^{-x/(\lambda+\delta_{0})}. $$