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Úprava zlomkových výrazov
Uprav a napíš podmienky:
\( \large\frac{{{{\left({a-\frac{1}{a}}\right)}^{-2}}+{{\left({a+\frac{1}{a}}\right)}^{-2}}}}{{{{\left({a-\frac{1}{a}}\right)}^{-2}}-{{\left({a+\frac{1}{a}}\right)}^{-2}}}} \)
\( \large=\frac{2\left(a^2+\frac{1}{a^2}\right)}{4}=\frac{\frac{a^{4+1}}{a^2}}{2}=\frac{a^4+1}{2a^2} \)
\( \normalsize a\neq0,a\neq\pm1 \)
\( \large=\frac{2\left(a^2+\frac{1}{a^2}\right)}{4}=\frac{\frac{a^{4+1}}{a^2}}{2}=\frac{a^4-1}{2a^2} \)
\( \normalsize a\neq0,a\neq\pm1 \)
\( \large=\frac{2\left(a^2+\frac{1}{a^2}\right)}{4}=\frac{\frac{a^{4+1}}{a^2}}{2}=\frac{a^4+1}{4a^2} \)
\( \normalsize a\neq0,a\neq\pm1 \)
\( \large=\frac{2\left(a^2+\frac{1}{a^2}\right)}{4}=\frac{\frac{a^{4+1}}{a^2}}{2}=\frac{a^4+2}{2a^2} \)
\( \normalsize a\neq0,a\neq\pm1 \)