we have the expression
[tex]\frac{2x+10x+12}{x^2+3x+2}[/tex]Combine like terms in the numerator
[tex]2x+10x+12=12x+12=12(x+1)[/tex]Simplify the denominator
[tex]x^2+3x+2=(x+2)(x+1)[/tex]substitute in the original expression
[tex]\frac{12(x+1)}{(x+1)(x+2)}=\frac{12}{x+2}[/tex]