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Uprava lomeného výrazu
Uprav v \( \R \) lomený výraz a urč podmienky:
\( \large\frac{u^2+v^2}{\left(u+v\right)^2}+\frac{\frac{2}{uv}}{\left(\frac{1}{u}+\frac{1}{v}\right)^2} \)
\( \large=\frac{\frac{u^2+2uv+v^2}{\left(uv\right)^2}}{\frac{u^2+2uv+v^2}{\left(uv\right)}}= \)
\( =1 \)
\( \normalsize u\neq-v,u\neq0,v\neq0 \)
\( \large=\frac{\frac{u^2+2uv+v^2}{\left(uv\right)^2}}{\frac{u^2+2uv+v^2}{\left(u^2v^2\right)}}= \)
\( =1 \)
\( \normalsize u\neq-v,u\neq0,v\neq0 \)
\( \large=\frac{\frac{u^2+2uv+v^2}{\left(uv\right)^2}}{\frac{u^2+v^2}{\left(uv\right)^2}}= \)
\( =1 \)
\( \normalsize u\neq-v,u\neq0,v\neq0 \)
\( \large=\frac{\frac{u^2+2uv+v^2}{\left(uv\right)^2}}{\frac{u^2+2uv+v^2}{\left(uv\right)^2}}= \)
\( =1 \)
\( \normalsize u\neq-v,u\neq0,v\neq0 \)