Problem
The partial fraction decomposition of $\frac{10}{(x-1)(x+1)}$ can be written in the form of $\frac{f(x)}{x-1}+\frac{g(x)}{x+1}$, where \[ \begin{array}{l} f(x)= \\ g(x)= \end{array} \] Question Help: $\square$ Video Submit Question Jump to Answer
Solution
Step 1 ：Multiplying both sides by $(x-1)(x+1)$ gives us $$10 = f(x)(x+1)+g(x)(x-1).$$
Step 2 ：Setting $x=1$ gives $10=2f(1)$, and so $f(1)=5$.
Step 3 ：Setting $x=-1$ gives $10=-2g(-1)$, and so $g(-1)=-5$.
Step 4 ：Therefore, $f(x)=5$ and $g(x)=-5$.
