Odpowiedź:
[tex]a)\ \ 4p(\frac{1}{2}p-\frac{1}{3})-3p(\frac{1}{6}p+\frac{1}{9})=\frac{4}{2}p^2-\frac{4}{3}p-\frac{3}{6}p^2-\frac{3}{9}p=2p^2-\frac{4}{3}p-\frac{1}{2}p^2-\frac{1}{3}p=\\\\=1\frac{1}{2}p^2-\frac{5}{3}p=1\frac{1}{2}p^2-1\frac{2}{3}p\\\\\\b)\ \ -5(\frac{1}{4}x+\frac{1}{2}y)+3(\frac{3}{4}x-\frac{1}{2}y)=-\frac{5}{4}x-\frac{5}{2}y+\frac{9}{4}x-\frac{3}{2}y=\frac{4}{4}x-\frac{8}{2}y=x-4y[/tex]
[tex]c)\ \ (\frac{1}{2}m-\frac{1}{5}):2+(\frac{1}{2}m+\frac{2}{5}):4=(\frac{1}{2}m-\frac{1}{5})\cdot\frac{1}{2}+(\frac{1}{2}m+\frac{2}{5})\cdot\frac{1}{4}=\\\\=\frac{1}{4}m-\frac{1}{10}+\frac{1}{8}m+\frac{2}{20}=\frac{1}{4}m+\frac{1}{8}m-\frac{1}{10}+\frac{2}{20}= \frac{2}{8}m+\frac{1}{8}m-\frac{2}{20}+\frac{2}{20}=\frac{3}{8}m[/tex]
[tex]d)\ \ (\frac{2}{3}a+\frac{3}{4}b):6-(\frac{1}{3}a+\frac{1}{2}b):4=(\frac{2}{3}a+\frac{3}{4}b)\cdot\frac{1}{6}-(\frac{1}{3}a+\frac{1}{2}b)\cdot\frac{1}{4}=\\\\=\frac{2}{18}a+\frac{3}{24}b-\frac{1}{12}a-\frac{1}{8}b=\frac{1}{9}a+\frac{1}{8}b-\frac{1}{12}a-\frac{1}{8}b=\frac{4}{36}a-\frac{3}{36}a=\frac{1}{36}a[/tex]
[tex]e)\ \ 6(\frac{1}{9}u+\frac{1}{12})-(\frac{1}{2}u+\frac{3}{4}):3=\frac{6}{9}u+\frac{6}{12}-(\frac{1}{2}u+\frac{3}{4})\cdot\frac{1}{3}=\frac{2}{3}u+\frac{1}{2}-\frac{1}{6}u-\frac{3}{12}=\\\\=\frac{2}{3}u-\frac{1}{6}u+\frac{1}{2}-\frac{1}{4}=\frac{4}{6}u-\frac{1}{6}u+\frac{2}{4}-\frac{1}{4}=\frac{3}{6}u+\frac{1}{4}=\frac{1}{2}u+\frac{1}{4}[/tex]
