Let's factorise the denominator
#x^2+2x-3=(x-1)(x+3)#
Let #f(x)=(x+1)^2/((x-1)(x+3))#
The domain of #f(x)# is #D_f(x)=RR-{-3,1}#
The numerator is #>0, AA x in D_f(x)#
Now, we can do the sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaa)##1##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x+3##color(white)(aaaa)##-##color(white)(aaaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-1##color(white)(aaaa)##-##color(white)(aaaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaaaa)##-##color(white)(aaaa)##+#
So,
# f(x)>=0 # when # x in ] -3,1 [ # or #-3< x < 1 #
Let # graph{y=(x+1)^2/((x-1)(x+3)) [-12.66, 12.65, -6.33, 6.33]} #