Answer
It doesn't make sense
Work Step by Step
We have to simplify the given rational expression (if possible):
$$\dfrac{2(x+2)-5(x+1)}{(x+2)(x+1)}.$$
Dividing the numerator and the denominator of a rational function by the denominator does not lead to a simplified fraction. It is the same thing as if we would rewrite the function as a sum of fractions and then simplify each of them separately:
$$\begin{align*}
\dfrac{2(x+2)-5(x+1)}{(x+2)(x+1)}&=\dfrac{2(x+2)}{(x+2)(x+1)}-\dfrac{5(x+1)}{(x+2)(x+1)}\\
&=\dfrac{2}{x+1}-\dfrac{5}{x+2}.
\end{align*}$$
So it makes little sense to divide the numerator by the denominator
(and obtain the above decomposition) and to divide the denominator by the denominator and obtain $1$.
The most common approach to obtain a simplified fraction is to first factor both numerator and denominator and afterwards look for common factors and simplify them.
$$\dfrac{2(x+2)-5(x+1)}{(x+2)(x+1)}=\dfrac{2x+4-5x-5}{(x+2)(x+1)}=\dfrac{-3x-1}{(x+2)(x+1)}.$$
We cannot simplify further.
