Úprava zlomku v reálných číslech
Uprav v \mathbb{R} a urči podmínky:
\large \Large \frac{{x^{2}-4}}{{x^{2}-x-6}}\large
\frac{{x^{2}\ –\ 4}}{{x^{2}\ –\ x\ –\ 6}} = \frac{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 2} \right)}}{{\left( {x\ +\ 3} \right)\ \cdot\ \left( {x\ –\ 3} \right)}} = \frac{x\ –\ 2}{x\ –\ 3}
\large x \neq 3,x \neq- 3
\frac{{x^{2}\ –\ 4}}{{x^{2}\ –\ x\ –\ 6}} = \frac{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 2} \right)}}{{\left( {x\ +\ 1} \right)\ \cdot\ \left( {x\ –\ 3} \right)}} = \frac{x\ –\ 2}{x\ –\ 3}
\large x \neq 3,x \neq- 1
\frac{{x^{2}\ –\ 4}}{{x^{2}\ –\ x\ –\ 6}} = \frac{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 2} \right)}}{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 3} \right)}} = \frac{x\ –\ 2}{x\ –\ 3}
\large x \neq 3,x \neq- 2
\frac{{x^{2}\ –\ 4}}{{x^{2}\ –\ x\ –\ 6}} = \frac{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 2} \right)}}{{\left( {x\ +\ 2} \right)\ \cdot\ \left( {x\ –\ 4} \right)}} = \frac{x\ –\ 2}{x\ –\ 4}
\large x \neq 4,x \neq- 2