a: \(A=\dfrac{5x^3y^2-7x^2y^3+6xy^4}{-2x^ny^m}\)
\(=-\dfrac{5x^3y^2}{2x^ny^m}+\dfrac{7x^2y^3}{2x^ny^m}-\dfrac{6xy^4}{2x^ny^m}\)
\(=-\dfrac{5}{2}\cdot x^{3-n}\cdot y^{2-m}+\dfrac{7}{2}\cdot x^{2-n}\cdot y^{3-m}-3x^{1-n}y^{4-m}\)
\(=x^{1-n}\cdot y^{2-m}\left(-\dfrac{5}{2}x^2+\dfrac{7}{2}xy-3y^2\right)\)
Để A chia hết cho B thì \(\left\{{}\begin{matrix}1-n>=0\\2-m>=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}n< =1\\m< =2\end{matrix}\right.\)
mà n,m là các số tự nhiên lớn nhất có thể
nên n=1;m=2
b: Khi n=1;m=2 thì \(\dfrac{A}{B}=x^{1-1}\cdot y^{2-2}\cdot\left(-\dfrac{5}{2}x^2+\dfrac{7}{2}xy-3y^2\right)\)
\(=x^0\cdot y^0\cdot\left(-\dfrac{5}{2}x^2+\dfrac{7}{2}xy-3y^2\right)=-\dfrac{5}{2}x^2+\dfrac{7}{2}xy-3y^2\)
