19. What is the positive difference between the numerator and the denominator when the expression shown is written as a single fraction in its simplest form?
A $2 n+2$
B $n+2$
C $n$
D 2
E 1
$$
\frac{n}{n+1-\frac{n+2}{n+3}}
$$
19. E Multiplying the numerator and denominator by $n+3$ :
$$
\frac{n}{n+1-\frac{n+2}{n+3}}=\frac{n(n+3)}{(n+1)(n+3)-(n+2)}=\frac{n^{2}+3 n}{n^{2}+4 n+3-n-2}=\frac{n^{2}+3 n}{n^{2}+3 n+1} \text {. }
$$

Therefore the difference between the numerator and denominator of the simplified fraction is 1 .