How can i view the poles of a function more strong?

edit

Hi, I'm drawing a rational function and i use plot wit detect_poles='show', but i can hardly view the poles, how can i view the poles with a best view? Here is my sagemath code:

f5(x)=(x^2+3*x+11)/(x+1)
d1f5(x) = f5.derivative(x,1)
umd15= d1f5(x).full_simplify()
print(umd15)
d2f5(x) = f5.derivative(x,2)
umd25= d2f5(x).full_simplify()
print(umd25)
Singular25=solve(umd15==0,x)
#Inflexion25=solve(umd25==0,x)
lista_singular25 = umd15.roots(x)
#lista_inflex25=umd25.roots(x)
for raiz5 in lista_singular25:
    print("Punto Singular = ({0},{1})".format(raiz5[0], f5(raiz5[0])))
#for raizz5 in lista_inflex25:
#    print("Punto Inflexión = ({0},{1})".format(raizz5[0], f5(raizz5[0])))
fig5=plot([f5(x),point(((-4,-5),(2,7),),rgbcolor=hue(1),size='40')],(-8.5,8.5),detect_poles='show', thickness=2.0, xmin=-8,xmax=8,ymin=-10,ymax=10,ticks=[1,1])
fig5 += text('P(-4,-5)', (-4.5,-5.7), color='red')
fig5 += text('Q(2,7)', (2,8), color='red')
fig5 += plot([x+2],(-8.5,8.5),color='green',linestyle='--',thickness=2.0)
fig5 += text('y=x+2', (8,8), color='red',clip='yes')
fig5.axes_labels([r'$x$', r'$\frac{(x^2+3x+11)}{(x+1)}$'])
fig5.show()

I want an improve viewing about the vertical asymptotic x=-1

Thanks