Aufgabenstellung: \(\frac{8x^{2}y+12xy^{2}}{10x^{2}}\div \frac{-4x^{3}y-6y^{2}x^{2}}{25xy^{2}}\)
Lösung:
\(\frac{8x^{2}y+12xy^{2}}{10x^{2}}\div \frac{-4x^{3}y-6y^{2}x^{2}}{25xy^{2}}=\frac{8x^{2}y+12xy^{2}}{10x^{2}}\cdot \frac{25xy^{2}}{-4x^{3}y-6y^{2}x^{2}}\)
\(=\frac{4xy\left ( 2x+3y \right )}{-2x^{2}\left ( 2x+3y \right )}\cdot \frac{5y^{2}}{2x}=\frac{2}{-x}\cdot \frac{5y^{2}}{2x}\)
\(=\underline{\underline{-\frac{5y^{2}}{x^{2}}}}\)