$$f(x)= \frac{x}{(1-x)^2}$$
I have been trying to sketch functions with a repeated root in the denominator. However, I cannot do it as I struggle to find where $x$ intersects the graph and the shape of it as I cannot split it into partial fractions. I am unsure whether there is another method of doing these particular ones.
A good method I use to plot graphs:
A) Domain
B) Intercepts $x,y=0?$
C) Symmetry/Periodicity:
Symmetry: If $f(-x)=f(x)$ on the domain then it is EVEN (symmetric about y axis).
Or $f(-x)=-f(x)$ on domain then it is ODD (symmetric about the origin).
Can be neither odd or even.
Periodicity: Where $f(x+p)=f(x)$ where $p$ is a positive constant.
D) Asymptotes (horizontal/vertical)
E) Intervals of increase or decrease ($f'(x)$)
F) Local Min/Max or Inflection ($f'(x)=0$)
G) Concavity ($f''(x)$)
For your case; $x=0$, then $y=0$
All these will help you determine shape, you do not necessarily need partial fractions!