## Functions Modeling Change: A Preparation for Calculus, 5th Edition

$\frac{a^2+b^2}{a^4b^2+a^2b^4}$
Since $\frac{a^2b^2}{a^2b^2}=1$, the expression can be multiplied to the original expression to get a simplified expression of $$=\frac{a^2b^2}{a^2b^2} \cdot \frac{a^{-2}+b^{-2}}{a^2+b^2}=\frac{a^2(a^{-2})b^2+b^2(b^{-2})a^2}{a^2(a^2)b^2+b^2(b^2)a^2}=\frac{a^2+b^2}{a^4b^2+a^2b^4}$$