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-\frac{35}{21}-\frac{69}{21}
Least common multiple of 3 and 7 is 21. Convert -\frac{5}{3} and \frac{23}{7} to fractions with denominator 21.
\frac{-35-69}{21}
Since -\frac{35}{21} and \frac{69}{21} have the same denominator, subtract them by subtracting their numerators.
-\frac{104}{21}
Subtract 69 from -35 to get -104.