Để tránh nhầm lẫn ta đặt \(P=\frac{M}{N}\) và biến đổi tử \(M\) và mẫu \(N.\)
\(M=\frac{4m^2+21}{2-2m}-6=\frac{4m^2+21-12+12m}{2\left(1-m\right)}=\frac{4m^2+12m+9}{2\left(1-m\right)}=\frac{\left(2m+3\right)^2}{2\left(1-m\right)}\)
\(N=\frac{2mn+3n-4m-6}{2-2m^2}=\frac{n\left(2m+3\right)-2\left(2m+3\right)}{2\left(1-m\right)\left(1+m\right)}=\frac{\left(2m+3\right)\left(n-2\right)}{2\left(1-m\right)\left(1+m\right)}\)
\(P=\frac{M}{N}=\frac{\left(2m+3\right)^2}{2\left(1-m\right)}:\frac{\left(2m+3\right)\left(n-2\right)}{2\left(1-m\right)\left(1+m\right)}\)
\(=\frac{\left(2m+3\right)^2}{2\left(1-m\right)}.\frac{2\left(1-m\right)\left(1+m\right)}{\left(2m+3\right)\left(n-2\right)}\)
\(\Rightarrow P=\frac{\left(2m+3\right)\left(1+m\right)}{n-2}\).
