Answer: Simplified form will be
[tex]\frac{2(x+2)}{(x-10}[/tex]
Explanation:
Since we have given that
[tex]\frac{2x^2+20x+32}{x^2-2x-80}[/tex]
and we need to simplify it,
First we take 2 as common factor from the numerator,
So, it becomes,
[tex]\frac{2(x^2+10x+16)}{x^2-2x-80}[/tex]
By using splitting the middle terms, we get
[tex]\frac{2(x^2+8x+2x+16)}{x^2-10x+8x-80}\\\\=\frac{2[(x(x+8)+2(x+8)]}{x(x-10)+8(x-10)}\frac{2(x+8)(x+2)}{(x-10)(x+8)}\\\\=\frac{2(x+2)}{(x-10}[/tex]
Hence, Simplified form will be
[tex]\frac{2(x+2)}{(x-10}[/tex]
