Question

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Answer 1

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

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