Пожалуйста помоги очень срочно надо)))

Знаменатель не может быть равен нулю (на ноль делить нельзя)

8. а) $frac{5x-75x^2}{x^2 +8}; x^2 +8 neq 0; x^2 +8 textgreater 0 x in (-infty;+infty)$

б) $frac{5a-4}{a^2-100}; a^2 -100 neq 0; (a-10) cdot (a+10) neq 0 a neq 10; a neq -10; x in (-infty; -10) cup (-10; 10) cup (10; +infty)$

в) $frac{y^4-81}{(y^3+6y^2) cdot (y^2 -121)}; y^3 +6y^2 neq 0; y^2 cdot (y+6) neq 0; y^2 neq 0; y neq 0; y neq -6; (y^2-121) neq 0; (y-11) cdot (y+11) neq 0; y neq 11; y neq -11 y in (-infty; -11) cup (-11; -6) cup (-6; 0) cup (0;11) cup (11; +infty)$

г) $frac{b+9}{b^2}; b^2 neq 0; b neq 0; b in (-infty;0) cup (0; +infty)$

д) $frac{x-7x^5}{(3-7x) cdot (2x+1)}; 3-7x neq 0; 7x neq 3; x neq frac{3}{7}; 2x+1 neq 0; 2x neq -1; x neq -frac{1}{2} x in (-infty;-frac{1}{2}) cup (-frac{1}{2}; frac{3}{7}) cup (frac{3}{7}; + infty)$

9. а) $frac{14a^4}{5xy} cdot frac{10x^2 y^3}{21 a^2 b^3}=frac{2}{5 cdot 3 b^3} cdot a^{4-2} cdot x^{2-1} cdot y^{3-1}=frac{2 a^2xy^2}{15b^3}$

б) $frac{25m^2 -4n^2 }{15mn} : frac{25m^2 + 20mn + 4n^2}{9m^2}=frac{(5m-2n) cdot (5m+2n)}{15mn} cdot frac{9m^2}{(5m)^2 + 2 cdot 5 cdot 2 cdot mn + (2n)^2}= =frac{(5m-2n) cdot (5m+2n)}{15mn} cdot frac{9m^2}{(5m+2n)^2 }=frac{(5m-2n) cdot 3m}{5n cdot (5m+2n)}$

в) $frac{3y^2}{x cdot (x^3-y^3)}+frac{y}{x cdot (x^2 + xy + y^2) }-frac{1}{x cdot (x-y)}= = frac{3y^2}{x cdot (x-y) cdot (x^2+xy+y^2 )}+frac{y}{x cdot (x^2 + xy + y^2) }-frac{1}{x cdot (x-y)}=frac{3y^2 +y cdot (x-y)-(x^2+xy+y^2)}{x cdot (x-y) cdot (x^2 +xy +y^2)} =frac{3y^2 +xy -y^2 -x^2 -xy -y^2}{x cdot (x-y) cdot (x^2 +xy +y^2)}=frac{y^2-x^2 }{x cdot (x-y) cdot (x^2 +xy +y^2)}=frac{(y-x) cdot (y+x)}{x cdot (x-y) cdot (x^2 +xy +y^2)}=$ $= -frac{y+x}{x cdot (x^2 +xy +y^2)}$

г) $frac{(x+y) cdot (x^2 -xy +y^2 )}{x-y} cdot frac{(x-y) cdot (x^2 +xy+y^2)}{x+y}=(x^2-xy+y^2)cdot(x^2+xy+y^2)= = x^4+x^2y^2 + y^4$

10) а) $(frac{8}{2a cdot (a - 4)} -frac{3a +32}{(a-4) cdot (a^2 +4a+16)}) : frac{a-8}{a cdot (a^2 + 4a + 16)} -frac{4}{-(a-4)}= =frac{8cdot (a^2 +4a+16)-2a cdot (3a+32)}{2a cdot (a-4) cdot (a^2 +4a+16)} cdot frac{a cdot (a^2 +4a+16)}{a-8}+frac{4}{a-4}= = frac{8a^2 +32a+128-6a^2 -64a}{2 cdot (a-4)} cdot frac{1}{a-8}+frac{4}{a-4} = frac{2a^2 -32a+4 cdot 2 cdot(a-8)}{2 cdot (a-4) cdot (a-8) (a-4)}= frac{2a^2 -32a+8a-64}{2 (a-4) (a-8)} = frac{2 a^2 -24a-64}{2 (a-4) (a-8)}$ $= frac{2 cdo (a^2 -12a-32)}{2 (a-4) (a-8)}=frac{(a-4) cdot (a-8)}{(a-4) cdot (a-8)}=1$

б) $frac{(x+y) cdot (x^2 -xy+y^2 )}{x+y} cdot frac{1}{(x-y) cdot (x+y)} + frac{2y}{x+y}-frac{xy}{(x-y) cdot (x+y)}= = frac{x^2 -xy+y^2}{(x-y)(x+y)}+frac{2y}{x+y}-frac{xy}{(x-y) cdot (x+y)}=frac{x^2 -xy+y^2 +2y cdot (x-y)-xy}{(x-y) cdot (x+y)}= =frac{x^2 -xy +y^2 +2xy-2y^2 -xy}{(x-y) cdot (x+y)}=frac{x^2 -y^2}{(x-y) cdot (x+y)}=frac{(x-y) cdot (x+y)}{(x-y) cdot (x+y)}=1$