Question

2/15/1/5x-1/3-1/12=1/24 решите уравнение

Answer 1

$\frac{ \frac{2}{15} }{ \frac{1}{5x} } - \frac{1}{3} - \frac{1}{12} = \frac{1}{24} \\ \\ \frac{2}{15} : \frac{1}{5x} = \frac{1}{24} + \frac{1*8}{3*8} + \frac{1*2}{12*2} \\ \\ \frac{2}{15} * \frac{5x}{1} = \frac{11}{24} \\ \\ \frac{2x}{3} = \frac{11}{24} \\ \\ 2x*24 = 3*11 \\ 48x=33 \\ x= \frac{33}{48} = \frac{11}{16}$

Проверим:
$\frac{ \frac{2}{15} }{ \frac{1}{5* \frac{11}{16} } } - \frac{1}{3} - \frac{1}{12}= \frac{1}{24} \\ \\ \frac{2}{15} : \frac{1}{ \frac{55}{16} } - \frac{4}{12} - \frac{1}{12} = \frac{1}{24} \\ \\ \frac{2}{15} : \frac{16}{55} - \frac{5}{12} = \frac{1}{24} \\ \\ \frac{2*55}{15*16} - \frac{5}{12} = \frac{1}{24} \\ \\ \frac{1*11}{3*8} - \frac{5*2}{12*2} = \frac{1}{24} \\ \\ \frac{11-10}{24} = \frac{1}{24} \\ \\ \frac{1}{24} = \frac{1}{24}$