a) \(\frac{a^2m-a^2n-b^2n+b^2m}{a^2+b^2}=\frac{a^2\left(m-n\right)+b^2\left(m-n\right)}{a^2+b^2}\)
\(=\frac{\left(m-n\right)\left(a^2+b^2\right)}{a^2+b^2}=m-n\)
b) \(\frac{\left(ab+bc+cd+ad\right)abcd}{\left(c+d\right)\left(a+b\right)+\left(b-c\right)\left(a-b\right)}\)
\(=\frac{\left[b.\left(a+c\right)+d.\left(a+c\right)\right].abcd}{ac+bc+da+db+ab-b^2-ca+bc}\)
\(=\frac{\left(a+c\right)\left(d+b\right)abcd}{2bc+da+db+ab-b^2}\)