Explanation:
The given expression is
[tex]\frac{x^2+7x+10}{x^2+4x+4}\cdot\frac{x^2+3x+2}{x^2+6x+5}[/tex]Then, to simplify, we need to factorize each polynomial as
x² + 7x + 10 = (x + 2)(x + 5)
x² + 4x + 4 = (x + 2)(x + 2)
x² + 3x + 2 = (x + 1)(x + 2)
x² + 6x + 5 = (x + 5)(x + 1)
So, the first step is to replace each expression with their factors
[tex]\frac{(x+2)(x+5)}{(x+2)(x+2)}\cdot\frac{(x+1)(x+2)}{(x+5)(x+1)}[/tex]Now, we can simplify the fractions, so
[tex]\frac{(x+5)}{(x+2)}\cdot\frac{(x+2)}{(x+5)}[/tex]Then, multiply the fractions and simplify
[tex]\begin{gathered} \frac{(x+5)(x+2)}{(x+2)(x+5)} \\ \\ 1 \end{gathered}[/tex]Answer:
Therefore, the answer is
