Brudden brøk

$$=\frac{{\displaystyle \frac{2·{\displaystyle \stackrel{3}{\cancel{21}}}}{\cancel{7}}}}{{\displaystyle \frac{5·\stackrel{7}{\cancel{21}}}{\cancel{3}}}}=\frac{6}{35}$$

$$=\frac{{\displaystyle \frac{3·12}{4}+3·12}}{5·12-{\displaystyle \frac{2·12}{3}}}=\frac{9+36}{60-8}=\frac{45}{52}$$

$$\begin{array}{rcl}& =& \frac{{\displaystyle \frac{7·36}{18}-1·36-\frac{1·36}{6}+\frac{3·36}{12}}}{{\displaystyle \frac{7·36}{9}-\frac{13·36}{4}}}\\ & & \\ & =& \frac{14-36-6+9}{28-117}=\frac{-19}{-89}=\frac{19}{89}\end{array}$$

$$\begin{array}{rcl}& = & \frac{{\displaystyle \frac{2·\cancel{30}}{\cancel{30}}-1·30-\frac{1·{\displaystyle \stackrel{10}{\cancel{30}}}}{\cancel{3}}+\frac{2·{\displaystyle \stackrel{2}{\cancel{30}}}}{\cancel{15}}}}{{\displaystyle \frac{7·{\displaystyle \stackrel{5}{\cancel{30}}}}{\cancel{6}}-\frac{3·{\displaystyle \stackrel{6}{\cancel{30}}}}{\cancel{5}}}}\\ & & \\ & =& \frac{2-30-10+4}{35-18}=\frac{{\displaystyle \stackrel{2}{\cancel{34}}}}{\cancel{17}}=-2\end{array}$$

$$\frac{{\displaystyle \frac{3·\cancel{42}}{\cancel{42}}+1·42-\frac{1·{\displaystyle \stackrel{14}{\cancel{42}}}}{\cancel{3}}}}{{\displaystyle \frac{7·{\displaystyle \stackrel{7}{\cancel{42}}}}{\cancel{6}}-\frac{3·{\displaystyle \stackrel{6}{\cancel{42}}}}{\cancel{7}}}}=\frac{3+42-14}{49-18}=\frac{31}{31}=1$$