faster way?

\(\displaystyle \frac{x^2+10}{(x^2+4)(x^2+1)} = \frac{-2}{x^2+4} + \frac{3}{x^2+1}\)

\(\displaystyle \frac{x^2+10}{(x^2+4)(x^2+1)} = \frac{-2(x^2+1)}{(x^2+4)(x^2+1)} + \frac{3(x^2+4)}{(x^2+4)(x^2+1)}\)

numerator forms the equation ...

\(\displaystyle x^2+10 = -2(x^2+1) + 3(x^2+4)\)

\(\displaystyle 10 = 10\)

solution set ... $x \in \mathbb{R}$