[tex]\dfrac{4x^2-4x-8}{2x-2}=\dfrac{4\left(x^2-x-2\right)}{2(x-1)}\\\\=2\cdot\dfrac{(x-2)(x+1)}{x-1}\qquad\text{no factors cancel}\\\\=2x-\dfrac{4}{x-1}\qquad\text{curve with slant, vertical asymptotes}[/tex]
