Example 5. For the equation $(1989 x)^{2}-1988 \cdot 1990 x$ $-1=0$, the larger root is $r$. For the equation $x^{2}+1989 x-1990=0$, the smaller root is $s$. Find the value of $r-s$. (Adapted from the 1984 Beijing Mathematics Competition)
Solve the equation $(1989 x)^{2}-1988 \cdot 1990 x-1$ $=0$, we get
$(1989 x)^{2}-(1989-1)(1989+1) x-1=0$.
Obviously, $1989^{2}-(1989-1)(1989+1)-1$ $=0$, so the equation has one root $x_{1}=1$, then the other root is $\boldsymbol{x}_{2}=-\frac{1}{1989^{2}}$, thus the larger root $r=1$.

Similarly, for the equation $x^{2}+1989 x-1990=0$, the sum of the coefficients is 0, so it also has one root $x_{1}=1$. Then the other root is $x_{2}=-1990$. Therefore, $s=-1990$.
Hence $r-s=1-(-1990)=1991$.