Rovnica s neznámou a parametrom
Rieš s neznámou \( x \in \mathbb{R} \) a parametrom \( p \in \mathbb{R} \) rovnicu \( \frac{2}{p(x-3)}+\frac{3}{(p-1)(x+1)}=\frac{x-5}{p(x+1)(x-3)} \).
\( \begin{array}{l}p\in\left\{\pm1;0;\frac{1}{4}\right\}\ldots\ldots\ldots\ldots.\ldots K=\emptyset\\ p\in\mathbb{R}-\left\{\pm1;0;\frac{1}{4}\right\}\ldots\ldots\ldots....K=\left\{\frac{2 p+7}{4 p-1}\right\}\end{array} \)
\( \begin{array}{l}p\in\left\{\pm3;0;\frac{1}{5}\right\}\ldots\ldots\ldots\ldots.\ldots K=\emptyset\\ p\in\mathbb{R}-\left\{\pm3;0;\frac{1}{5}\right\}\ldots\ldots\ldots....K=\left\{\frac{4 p+9}{6 p-3}\right\}\end{array} \)
\( \begin{array}{l}p\in\left\{\pm4;0;\frac{1}{6}\right\}\ldots\ldots\ldots\ldots.\ldots K=\emptyset\\ p\in\mathbb{R}-\left\{\pm4;0;\frac{1}{6}\right\}\ldots\ldots\ldots....K=\left\{\frac{5 p+10}{7 p-4}\right\}\end{array} \)
\( \begin{array}{l}p\in\left\{\pm2;0;\frac{1}{3}\right\}\ldots\ldots\ldots\ldots.\ldots K=\emptyset\\ p\in\mathbb{R}-\left\{\pm2;0;\frac{1}{3}\right\}\ldots\ldots\ldots....K=\left\{\frac{3 p+8}{5 p-2}\right\}\end{array} \)