Úprava zlomku v reálných číslech
Uprav v \mathbb{R} a urči podmínky:
\large \Large \frac{a^{2}-b^{2}}{a^{2}}\large \cdot \Large \frac{a}{ \left( a+b \right) ^{2}}\large
\frac{a^{2}\ –\ b^{2}}{a^{2}}\cdot \frac{a}{\left (a\ +\ b \right )^{2}} = \frac{\left (a\ +\ b \right )\left (a\ –\ b \right )\ \cdot\ a}{a^{2}\ \cdot\ \left (a\ +\ b \right )^{2}}=
= \frac{a\ –\ b}{a\ \cdot\ \left (a\ –\ b \right )}
\large a \neq 0,a \neq- b
\frac{a^{2}\ –\ b^{2}}{a^{2}}\cdot \frac{a}{\left (a\ +\ b \right )^{2}} = \frac{\left (a\ +\ b \right )\left (a\ –\ b \right )\ \cdot\ a}{a^{2}\ \cdot\ \left (a\ +\ b \right )^{2}}=
= \frac{a\ –\ b}{a^{2}\ \cdot\ \left (a\ +\ b \right )}
\large a \neq 0,a \neq- b
\frac{a^{2}\ –\ b^{2}}{a^{2}}\cdot \frac{a}{\left (a\ +\ b \right )^{2}} = \frac{\left (a\ +\ b \right )\left (a\ –\ b \right )\ \cdot\ a}{a^{2}\ \cdot\ \left (a\ +\ b \right )^{2}}=
= \frac{a\ –\ b}{a\ \cdot\ \left (a\ +\ b \right )}
\large a \neq 0,a \neq- b
\frac{a^{2}\ –\ b^{2}}{a^{2}}\cdot \frac{a}{\left (a\ +\ b \right )^{2}} = \frac{\left (a\ +\ b \right )\left (a\ –\ b \right )\ \cdot\ a}{a^{2}\ \cdot\ \left (a\ +\ b \right )^{2}}=
= \frac{a\ +\ b}{a\ \cdot\ \left (a\ +\ b \right )}
\large a \neq 0,a \neq- b