Úprava zlomku v reálných číslech
Uprav v \mathbb{R} a urči podmínky:
\large \Large \frac{{x^{3}+y^{3}}}{{x^{2}-y^{2}}}\large
\frac{{x^{3}\ +\ y^{3}}}{{x^{2}\ –\ y^{2}}} = \frac{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x^{2}\ +\ xy\ +\ y^{2}} \right)}}{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x\ –\ y} \right)}} =
= \frac{x^2\ +\ xy\ + \ y^2}{x\ –\ y}
\large x \neq \pm y
\frac{{x^{3}\ +\ y^{3}}}{{x^{2}\ –\ y^{2}}} = \frac{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x^{2}\ –\ xy\ +\ y^{2}} \right)}}{{\left( {x\ –\ y} \right)\ \cdot\ \left( {x\ –\ y} \right)}} =
= \frac{x^2\ –\ xy\ + \ y^2}{x\ –\ y}
\large x \neq \pm y
\frac{{x^{3}\ +\ y^{3}}}{{x^{2}\ –\ y^{2}}} = \frac{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x^{2}\ –\ xy\ +\ y^{2}} \right)}}{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x\ –\ y} \right)}} =
= \frac{x^2\ –\ xy\ + \ y^2}{x\ –\ y}
\large x \neq \pm y
\frac{{x^{3}\ +\ y^{3}}}{{x^{2}\ –\ y^{2}}} = \frac{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x^{2}\ –\ xy\ +\ y^{2}} \right)}}{{\left( {x\ +\ y} \right)\ \cdot\ \left( {x\ +\ y} \right)}} =
= \frac{x^2\ –\ xy\ + \ y^2}{x\ +\ y}
\large x \neq \pm y