4 1/6 : (1/4 Х + 1 4/15) - 1 5/6 =2/3

[latex]4 \frac{1}{6} :( \frac{1}{4} x+1 \frac{4}{15} )-1 \frac{5}{6} = \frac{2}{3} \\ \\ \\ 4 \frac{1}{6} :( \frac{1}{4} x+1 \frac{4}{15} )= \frac{2}{3} +1 \frac{5}{6} \\ \\ \\ 4\frac{1}{6} :( \frac{1}{4} x+1 \frac{4}{15} )= \frac{4}{6} +\frac{11}{6} \\ \\ \\ 4\frac{1}{6} :( \frac{1}{4} x+1 \frac{4}{15} )= \frac{15}{6} \\ \\ \\ \frac{1}{4} x+1 \frac{4}{15} =4\frac{1}{6} : \frac{15}{6} \\ \\ \\[/latex] [latex]\frac{1}{4} x+1 \frac{4}{15} =\frac{25}{6}*\frac{6}{15} \\ \\ \\\frac{1}{4} x+1 \frac{4}{15} =\frac{25}{6}*\frac{6}{15} \\ \\ \\ \frac{1}{4} x =\frac{25}{15}-1 \frac{4}{15} \\ \\ \\\frac{1}{4} x =\frac{25}{15}-\frac{19}{15} \\ \\ \\x =\frac{6}{15}:\frac{1}{4} \\ \\ \\ x =\frac{6}{15}*\frac{4}{1} \\ \\ \\x =\frac{24}{15} \\ \\ \\x =1\frac{3}{5} [/latex]

4 ( 1/6 ) : ( 1/4Х + 1 ( 4/15 )) - 1 ( 5/6 ) = 2/3 ; 4 ( 1/6 ) : ( 1/4х + 1 ( 4/15 )) = ( 4/6 ) + 1 ( 5/6 ) ; 4 ( 1/6 ) : ( 1/4х + 1 ( 4/15 ) ) = 2 ( 1/2 ) ; 1/4Х + 1 ( 4/15 ) = 4 ( 1/6 ) : 2 ( 1/2 ) ; 1/4Х + 1 ( 4/15 ) = ( 25/6 ) : ( 5/2 ) ; 1/4х + 1 ( 4/15 ) = 5/3 ; 1/4х = 1 ( 2/3 ) - 1 ( 4/15 ) ; 1/4х = 1 ( 10/15 ) - 1 ( 4/15 ) ; 1/4х = 6/15 ; Х = 6/15 : 1/4 ; Х = 24/15 ; Х = 1 ( 9/15 )