Use partial fractions before sketching an absolute reciprocal

Curve C is $f(x)=(x-9)^2/[(x-3)(x+3)]$.

(i) Express it as $P+Q/(x-3)+R/(x+3)$.

(ii) State all asymptotes and axial intercepts.

(iii) Sketch separately (a) $y=f(x)$ and (b) $y=|1/f(x)|$, making the main features clear.