УПРОСТИТЬ ВЫРАЖЕНИЯ.
1. $( frac{b}{9a-a^3}- frac{1}{a^2+3a}+ frac{3}{a^2b-9b}): frac{b^2-6b+9}{a^3b-9ab}$
2. $(1- frac{1}{1-a}):(1- frac{1-2a^2}{1-a}+a)$
3. $frac{a^2+a-ab-b}{a^2+a+ab+b}: frac{a^2-a-ab+b}{a^2-a+ab-b}$
4. $( frac{6}{a^2+5a+4}- frac{2}{a^2+3a+2}+ frac{a}{a^2+6a+8})^2* frac{a^2+4a+4}{2}$
5. $frac{(ab^-^1+ a^{-1}b+1)(a^-^1-b^-^1)^2 }{a^2b^-^2+a^-^2b^2-(ab^-^1+a^-^1b)}$

$( frac{b}{9a-a^3}- frac{1}{a^2+3a}+ frac{3}{a^2b-9b}): frac{b^2-6b+9}{a^3b-9ab} = =( frac{b}{a(9-a^2)}- frac{1}{a(a+3)}+ frac{3}{b(a^2-9)}): frac{(b-3)^2}{ab(a^2-9)} = =( -frac{b}{a(a-3)(a+3)}- frac{1}{a(a+3)}+ frac{3}{b(a-3)(a+3)})cdot frac{ab(a^2-9)}{(b-3)^2} = =frac{-b^2-ab+3b+3a}{ab(a-3)(a+3)}cdot frac{ab(a^2-9)}{(b-3)^2} = frac{-b(b+a)+3(a+b)}{ab(a-3)(a+3)}cdot frac{ab(a^2-9)}{(b-3)^2} = =frac{(a+b)(3-b)ab(a^2-9)}{ab(a-3)(a+3)(3-b)^2} = frac{a+b}{3-b}$

$(1- frac{1}{1-a}):(1- frac{1-2a^2}{1-a}+a)= frac{1-a-1}{1-a}: frac{1-a-1+2a^2+a-a^2}{1-a}= =- frac{a}{1-a}: frac{a^2}{1-a}=- frac{a}{1-a}cdot frac{1-a}{a^2}=- frac{a}{2a^2}=- frac{1}{a}$

$frac{a^2+a-ab-b}{a^2+a+ab+b}: frac{a^2-a-ab+b}{a^2-a+ab-b} = frac{a(a+1)-b(a+1)}{a(a+1)+b(a+1)}: frac{a(a-1)-b(a-1)}{a(a-1)+b(a-1)} = = frac{(a+1)(a-b)}{(a+1)(a+b)}: frac{(a-1)(a-b)}{(a-1)(a+b)} = frac{a-b}{a+b}: frac{a-b}{a+b} = frac{a-b}{a+b}cdot frac{a+b}{a-b} =1$

$( frac{6}{a^2+5a+4}- frac{2}{a^2+3a+2}+ frac{a}{a^2+6a+8})^2cdot frac{a^2+4a+4}{2} = =( frac{6}{a^2+4a+a+4}- frac{2}{a^2+2a+a+2}+ frac{a}{a^2+4a+2a+8})^2cdotfrac{(a+2)^2}{2} = =( frac{6}{a(a+4)+a+4}- frac{2}{a(a+2)+a+2}+ frac{a}{a(a+4)+2(a+4)})^2cdotfrac{(a+2)^2}{2} = =( frac{6}{(a+4)(a+1)}- frac{2}{(a+2)(a+1)}+ frac{a}{(a+4)(a+2)})^2cdotfrac{(a+2)^2}{2} =$
$=( frac{6a+12-2a-8+a^2+a}{(a+4)(a+1)(a+2)})^2cdotfrac{(a+2)^2}{2} = ( frac{a^2+4a+a+4}{(a+4)(a+1)(a+2)})^2cdotfrac{(a+2)^2}{2} = =( frac{a(a+4)+a+4}{(a+4)(a+1)(a+2)})^2cdotfrac{(a+2)^2}{2} = ( frac{(a+4)(a+1)}{(a+4)(a+1)(a+2)})^2cdotfrac{(a+2)^2}{2} = =( frac{1}{a+2})^2cdotfrac{(a+2)^2}{2} = frac{1}{(a+2)^2}cdotfrac{(a+2)^2}{2} =frac{1}{2}$

$frac{(ab^-^1+ a^{-1}b+1)(a^-^1-b^-^1)^2 }{a^2b^-^2+a^-^2b^2-(ab^-^1+a^-^1b)} = dfrac{( frac{a}{b} + frac{b}{a} +1)( frac{1}{a} - frac{1}{b} )^2 }{ frac{a^2}{b^2} + frac{b^2}{a^2} -( frac{a}{b} + frac{b}{a} )} = dfrac{( frac{a^2+b^2+ab}{ab} )( frac{b-a}{ab})^2 }{ frac{a^4+b^4}{a^2b^2} -( frac{a^2+b^2}{ab} )} =dfrac{frac{a^2+b^2+ab}{ab}cdotfrac{(b-a)^2}{(ab)^2} }{ frac{a^4+b^4-ab(a^2+b^2)}{a^2b^2}} = frac{(a^2+b^2+ab)(b-a)^2}{ab(a^4+b^4-a^3b-ab^3)} =$
$= frac{(a^2+b^2+ab)(b-a)^2}{ab(a^3(a-b)-b^3(a-b))} = frac{(a^2+b^2+ab)(a-b)^2}{ab(a-b)(a^3-b^3)} = = frac{(a^2+b^2+ab)(a-b)^2}{ab(a-b)(a-b)(a^2+ab+b^2)} = frac{1}{ab}$