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Автор - papagenius

Пошаговое объяснение:

$ttdisplaystyle left({x+frac{5}{{12}}}right)-frac{9}{{20}}=frac{{11}}{{15}} hfill \left({x+frac{5}{{12}}}right)=frac{{11}}{{15}}+frac{9}{{20}}hfill\left({x+frac{5}{{12}}}right)=frac{{44}}{{60}}+frac{{27}}{{60}}hfill \left({x+frac{5}{{12}}}right)=frac{{71}}{{60}} hfill \x=frac{{71}}{{60}}-frac{5}{{12}} hfill \x=frac{{71}}{{60}}-frac{{25}}{{60}}=frac{{46}}{{60}}=boxed{frac{{23}}{{30}}} hfill \$

Проверка:

$ttdisplaystyle left( {frac{{46}}{{60}}+frac{5}{{12}}}right)-frac{9}{{20}}=frac{{46}}{{60}}+frac{{25}}{{60}}-frac{{27}}{{60}}=frac{{44}}{{60}}=frac{{11}}{{15}}$

$[begin{gathered}left( {x-frac{{11}}{{30}}} right)-frac{{16}}{{45}}=frac{2}{9} hfill \x-frac{{11}}{{30}}-frac{{16}}{{45}}=frac{2}{9} hfill \x=frac{2}{9}+frac{{16}}{{45}}+frac{{11}}{{30}} hfill \x=frac{{20}}{{90}}+frac{{32}}{{90}}+frac{{33}}{{30}} hfill \x=frac{{85}}{{90}}=boxed{frac{{17}}{{18}}} hfill \end{gathered} ]$

Проверка:

$ttdisplaystyle [left( {frac{{85}}{{90}}-frac{{11}}{{30}}} right)-frac{{16}}{{45}}=frac{{85}}{{90}}-frac{{33}}{{90}}-frac{{32}}{{90}}=frac{{20}}{{90}}=frac{2}{9}]$

$[begin{gathered}left( {x-frac{7}{{15}}} right)+frac{5}{8}=frac{{17}}{{24}} hfill \x-frac{7}{{15}}+frac{5}{8}=frac{{17}}{{24}} hfill \x=frac{{17}}{{24}}-frac{5}{8}+frac{7}{{15}} hfill \x=frac{{85}}{{120}}-frac{{75}}{{120}}+frac{{56}}{{120}} hfill \x=frac{{66}}{{120}}=boxed{frac{{11}}{{20}}} hfill \ end{gathered} ]$

Проверка:

$ttdisplaystyle [left( {frac{{66}}{{120}}-frac{7}{{15}}} right)+frac{5}{8}=frac{{66}}{{120}}-frac{{56}}{{120}}+frac{{75}}{{120}}=frac{{85}}{{120}}=frac{{17}}{{24}}]$

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