[tex] 1)\; \; \frac{12x+5y}{20x^2y}-\frac{5y-4x}{25xy^2}=\frac{5y(12x+5y)-4x(5y-4x)}{100x^2y^2}=\\\\=\frac{60xy+25y^2-20xy+16x^2}{100x^2y^2}=\frac{25y^2+40xy+16x^2}{100x^2y^2}=\frac{(5y+4x)^2}{10^2x^2y^2}=(\frac{5y+4x}{10xy})^2 [/tex]
[tex] 2)\; \; \frac{2n+3m}{12mn^2}-\frac{9m-2n}{18m^2n}=\frac{3m(2n+3m)-2n(9m-2n)}{36m^2n^2}=\\\\=\frac{6mn+9m^2-18mn+4n^2}{36m^2n^2}=\frac{9m^2-12mn+4n^2}{36m^2n^2}=\frac{(3m-2n)^2}{6^2m^2n^2}= (\frac{3m-2n}{6mn})^2 [/tex]
