algebra question

Sorry, can't read your LaTex !.

Let
$A = \dfrac{10^{1998} + 1}{10^{1999} + 1}$ and $B=\dfrac{10^{1999} + 1}{10^{2000} + 1}$

Which value is larger?

$\begin{array}{|rcll|} \hline \mathbf{B} &=& \mathbf{ \dfrac{10^{1999} + 1}{10^{2000} + 1} } \\\\ B &=& \dfrac{10*10^{1998} + 1}{10*10^{1999} + 1} \\\\ B &=& \dfrac{10*\left(10^{1998} + \frac{1}{10} \right)}{10*\left(10^{1999} + \frac{1}{10}\right)} \\\\ \mathbf{B} &=& \mathbf{ \dfrac{10^{1998} + \frac{1}{10} }{10^{1999} + \frac{1}{10}} } \\ \hline \end{array}$

$\Rightarrow A \gt B$