\(\frac{x^3+x^2-4x-4}{x^3+8x^2+17x+10}\)
\(=\frac{x^2\left(x+1\right)-4\left(x+1\right)}{x^3+x^2+7x^2+7x+10x+10}\)
\(=\frac{\left(x^2-4\right)\left(x+1\right)}{\left(x+1\right)\left(x^2+7x+10\right)}\)
\(=\frac{x^2-4}{x^2+7x+10}\)
\(=\frac{x^2-4}{x^2+5x+2x+10}\)
\(=\frac{\left(x-2\right)\left(x+2\right)}{x\left(x+5\right)+2\left(x+5\right)}\)
\(=\frac{x-2}{x+5}\)