factorisation of algebra homework question that asks to perform the multiplication and division and simplification.
$$\frac{x^2+7x+10}{x^2+5x+4} \times \frac{x^2+3x+2}{x^2+4x+4} =$$
$$\frac{(x+5)(x+2)}{(x+4)(x+1)} \times \frac{(x+1)(x+2)}{(x+2)(x+2)} =$$
$$ = \frac{(x+5)}{(x+4)}$$
is my working out and answer correct?
I am typing this extra sentence in order to meet your quality standards!!!

Yes, it is correct. The $x+2$'s and $x+1$ terms do cancel. If there was no multiplication, the second part would be $\frac{x+1}{x+2}$, and the left side would be as is. However, you're OK. 
