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Answer:
[tex]2\frac{7}{24x} + 5\frac{5}{6}[/tex]
Step-by-step explanation:
[tex]2 \frac{1}{8x}+ \frac{3}{4x} + \frac{1}{6} - \frac{7}{12x} + 5\frac{2}{3}[/tex]
find a common denominator for the x values: GCD = 24
so multiply each fraction with an x to get the common denominator
[tex]2 [(\frac{3}{3} )(\frac{1}{8x})] + [(\frac{6}{6})(\frac{3}{4x})] + \frac{1}{6} - [(\frac{2}{2})(\frac{7}{12x})] + 5\frac{2}{3}[/tex]
then multiply it out
[tex]2\frac{3}{24x} + \frac{18}{24x} + \frac{1}{6} - \frac{14}{24x} + 5\frac{2}{3}[/tex]
then, find the GCD for the fractions without x: GCD = 3
[tex]2\frac{3}{24x} + \frac{18}{24x} + \frac{1}{6} - \frac{14}{24x} + 5[(\frac{2}{2})( \frac{2}{3})][/tex]
then multiply it out
[tex]2\frac{3}{24x} + \frac{18}{24x} + \frac{1}{6} - \frac{14}{24x} + 5\frac{4}{6}[/tex]
finally, combine like terms:
[tex]2\frac{7}{24x} + 5\frac{5}{6}[/tex]