Hello I just need to review my results in this math problem

Answer:
To solve:
[tex]7\frac{2}{3}-(1\frac{2}{4}+3\frac{6}{8})[/tex]we get,
[tex]\frac{23}{3}-(\frac{6}{4}+\frac{30}{8})[/tex]Taking LCM of 4 and 8, we get LCM of 4,8 is 8
[tex]=\frac{23}{3}-(\frac{12+30}{8})[/tex][tex]=\frac{23}{3}-\frac{42}{8}[/tex]LCM of 3,8 is 24
[tex]=\frac{184-126}{24}[/tex][tex]=\frac{58}{24}[/tex][tex]=\frac{29}{12}[/tex][tex]=2\frac{5}{12}[/tex]Answer is:
[tex]=2\frac{5}{12}[/tex]