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[latex] \frac{a-b}{a^\frac{3}{4}+a^ \frac{1}{2}b^ \frac{1}{4} }- \frac{a^ \frac{1}{2}-b^ \frac{1}{2} }{a^ \frac{1}{4} +b^ \frac{1}{4} } = \frac{a-b}{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}- \frac{a^ \frac{1}{2}-b^ \frac{1}{2} }{a^ \frac{1}{4} +b^ \frac{1}{4} }=\frac{a-b-a^ \frac{1}{2} (a^ \frac{1}{2} -b^ \frac{1}{2}) }{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}= \\ \\ =\frac{a-b-a+a^ \frac{1}{2}b^ \frac{1}{2} }{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}=[/latex][latex]\frac{a^ \frac{1}{2}b^ \frac{1}{2}-b }{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}=\frac{b^ \frac{1}{2}( a^ \frac{1}{2}-b^ \frac{1}{2}) }{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}=\frac{b^ \frac{1}{2}( a^ \frac{1}{4}-b^ \frac{1}{4})( a^ \frac{1}{4}+b^ \frac{1}{4}) }{a^ \frac{1}{2}( a^\frac{1}{4}+b^ \frac{1}{4} )}=( \frac{b}{a} )^ \frac{1}{2}( a^ \frac{1}{4}-b^ \frac{1}{4}) }}[/latex] Если [latex]a= \frac{1}{16}, b= \frac{1}{81} [/latex], то [latex]( \frac{b}{a} )^ \frac{1}{2}( a^ \frac{1}{4}-b^ \frac{1}{4}) }}=( \frac{ \frac{1}{81} }{ \frac{1}{16} } )^ \frac{1}{2}( (\frac{1}{16} )^ \frac{1}{4}-(\frac{1}{81} )^ \frac{1}{4}) }}=( \frac{16 }{81} )^ \frac{1}{2}( \frac{1}{2} -\frac{1}{3} )= \\ \\ =\frac{4 }{9} ( \frac{3}{6} -\frac{2}{6} )=\frac{4 }{9} *\frac{1 }{6} =\frac{2}{27} [/latex]