\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-1\dfrac{7}{21}+\dfrac{2}{5}=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}-\dfrac{4}{3}\right)+\dfrac{2}{5}=1+\left(-1\right)+\dfrac{2}{5}=0+\dfrac{2}{5}=\dfrac{2}{5}\)

\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{32}{17}+\dfrac{2}{3}\) 

\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\dfrac{7}{21}+\dfrac{-32}{17}+\dfrac{2}{3}\) 

\(=1+\dfrac{1}{3}+\dfrac{-32}{17}+\dfrac{2}{3}\) 

\(=1+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\dfrac{-32}{17}\) 

\(=1+1+\dfrac{-32}{17}\) 

\(2+\dfrac{-32}{17}=\dfrac{2}{17}\)

15/34 + 7/21 + 19/34 - 20/15 + 3/7

= 3/7

\(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)

\(=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{7}{21}-\frac{20}{15}\right)+\frac{3}{7}\)

\(=1+1+\frac{3}{7}=2\frac{3}{7}=\frac{17}{7}\)

\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)

\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)

\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)

\(=1-1-\dfrac{15}{17}\)

\(=-\dfrac{15}{17}\)

\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)

= \(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-1\dfrac{15}{17}\)

= \(1+\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-1\dfrac{15}{17}\)

= \(1+1-1\dfrac{15}{17}\)

= \(2-1\dfrac{15}{17}\)

= \(\dfrac{2}{17}\)

\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{3}{1}+\dfrac{7}{21}+2\)

\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{7}{21}\right)-\left(3-2\right)\)

\(=1-1+\dfrac{14}{21}\)

\(=\dfrac{14}{21}\)

\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-3+\dfrac{7}{21}+2\)

= \(\dfrac{15}{34}+\dfrac{19}{34}+\dfrac{7}{21}+\dfrac{7}{21}-3+2\)

= \(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{7}{21}\right)-\left(3-2\right)\)

= \(1+\dfrac{2}{3}-1\)

= \(1-1+\dfrac{2}{3}\)

= \(\dfrac{2}{3}\)

GOOD LUCK!

\(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)

\(\frac{15}{34}+\frac{1}{3}+\frac{19}{34}+\left(-\frac{4}{3}\right)+\frac{3}{7}\)

\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{1}{3}-\frac{4}{3}\right)+\frac{3}{7}\)

\(1+\left(-1\right)+\frac{3}{7}\)

\(=0+\frac{3}{7}=\frac{3}{7}\)

\(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)

\(=\)\(\frac{15}{34}+\frac{1}{3}+\frac{19}{34}+\left(-\frac{4}{3}\right)+\frac{3}{7}\)

\(=\)\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{1}{3}-\frac{4}{3}\right)+\frac{3}{7}\)

\(=\)\(1+\left(-1\right)+\frac{3}{7}\)

\(=\)\(0+\frac{3}{7}\)

\(=\)\(\frac{3}{7}\)