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-\frac{2}{5}-\frac{4}{12}+\frac{4}{13}-\frac{13}{17}
Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.
-\frac{2}{5}-\frac{1}{3}+\frac{4}{13}-\frac{13}{17}
Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.
-\frac{6}{15}-\frac{5}{15}+\frac{4}{13}-\frac{13}{17}
Least common multiple of 5 and 3 is 15. Convert -\frac{2}{5} and \frac{1}{3} to fractions with denominator 15.
\frac{-6-5}{15}+\frac{4}{13}-\frac{13}{17}
Since -\frac{6}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.
-\frac{11}{15}+\frac{4}{13}-\frac{13}{17}
Subtract 5 from -6 to get -11.
-\frac{143}{195}+\frac{60}{195}-\frac{13}{17}
Least common multiple of 15 and 13 is 195. Convert -\frac{11}{15} and \frac{4}{13} to fractions with denominator 195.
\frac{-143+60}{195}-\frac{13}{17}
Since -\frac{143}{195} and \frac{60}{195} have the same denominator, add them by adding their numerators.
-\frac{83}{195}-\frac{13}{17}
Add -143 and 60 to get -83.
-\frac{1411}{3315}-\frac{2535}{3315}
Least common multiple of 195 and 17 is 3315. Convert -\frac{83}{195} and \frac{13}{17} to fractions with denominator 3315.
\frac{-1411-2535}{3315}
Since -\frac{1411}{3315} and \frac{2535}{3315} have the same denominator, subtract them by subtracting their numerators.
-\frac{3946}{3315}
Subtract 2535 from -1411 to get -3946.