Question

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Answer 1

$displaystyle 1)..frac{27a^{3}a^{2}}{b}:frac{18a^{4}}{7b^{2}}=frac{27a^{5}}{b}* frac{7b^{2}}{18a^{4}}=frac{21ab}{2}=10,5ab\\\2)..frac{3x^{2}}{5y^{3}}:frac{27x^{5}}{2y^{4}}*frac{5y}{3(x-1)}=frac{3x^{2}}{5y^{3}}*frac{2y^{4}}{27x^{5}}*frac{5y}{3(x-1)}=frac{2y^{2}}{27x^{3}(x-1)}\\\3)..(frac{x}{x+1}+1)*frac{1+x}{2x-1}=frac{2x+1}{x+1}*frac{x+1}{2x-1}=frac{2x+1}{2x-1}$

$displaystyle 4)..(frac{4a}{2-a}-a):frac{a+2}{a-2}=frac{4a-2a+a^{2}}{2-a}*frac{a-2}{a+2}= \ \ \ =-frac{a(a+2)(a-2)}{(a-2)(a+2)}=-a \ \ \ 5).. frac{xb+b^{2}}{7}: frac{b^{2}}{7x}+ frac{x+b}{b}= frac{b(x+b)}{7}* frac{7x}{b^{2}}+ frac{x+b}{b}= \ \ \ = frac{x(x+b)}{b}+ frac{x+b}{b}= frac{(x+b)(x+1)}{b}$