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