極限値を求める問題

$$ \begin{aligned} \hspace{10pt}& \lim_{x \rightarrow a}{ \frac{x^2 f(a)- a^2 f(x)}{x^2-a^2}}\\[1em] & = \lim_{x \rightarrow a}{ \frac{x^2 f(a) -a^2 f(a) + a^2 f(a)- a^2f(x)}{x^2-a^2}}\hspace{10pt}\\[1em] & = \lim_{x \rightarrow a}{ \frac{(x^2-a^2) f(a) - a^2( f(x) - f(a))}{x^2-a^2}}\\[1em] & = \lim_{x \rightarrow a}\left\{{f(a) - \frac{a^2}{x+a} \cdot\frac{ f(x) - f(a)}{x-a}}\right\}\\[1em] & = f(a) -\frac{a}{2}f'(a)\\[1em] \end{aligned} $$