The given expression is:
[tex]\frac{x^2-100}{2x+20}[/tex]
To simply the expression above, we are going to apply the difference of two squares rule for the numerator and we find the common factor for the denominator.
Thus, we have:
[tex]\begin{gathered} \frac{x^2-100}{2x+20} \\ \Rightarrow\frac{(x-10)(x+10)}{2(x+10)} \end{gathered}[/tex]
(x+10) is common to both the numerator and the denominator and as such, they will cancel out each other.
Thus, we have:
[tex]\begin{gathered} \frac{(x-10)(x+10)}{2(x+10)} \\ \Rightarrow\frac{x-10}{2} \end{gathered}[/tex]
Hence, the correct option is option A
