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[latex] \frac{18 x^{3} }{7b^{4}}* \frac{14b}{9 x^{2} }= \frac{2*2x}{b^{3} } [/latex] [latex] \frac{2}{9a^{2}-b^{2}} *(6a-2b)= \frac{2}{(3a-b)(3a+b)}*2(3a-b)= \frac{4}{3a+b} [/latex] [latex](- \frac{2a^{2} }{3b^{2} } )^{3}= - \frac{8a^{6} }{27b^{6} } [/latex] [latex] \frac{ x^{3}-16x }{3xy}* \frac{6y}{2x+8} = \frac{2x( x^{2} -16)}{2x(x+4)} = \frac{(x-4)(x+4)}{x+4}=x-4 [/latex] 2. [latex]- \frac{c^{3} +7c^{2} }{2b} : \frac{49- c^{2} }{4b^{2} } =- \frac{c^{2}(c+7) }{2b} * \frac{4b^{2} }{(7-c)(7+c)} =- \frac{2bc^{2} }{7-c} [/latex] [latex] \frac{3m-6n}{mn} : m^{2}-4mn+4n^{2}= \frac{3(m-2n)}{mn}* \frac{1}{(m-2n)(m-2n)}= \frac{3}{mn(m-2n)} [/latex] [latex] \frac{ax-3a}{2x+6} : \frac{9- x^{2} }{ x^{2} +6x+9}= \frac{a(x-3)}{2(x+3)}* \frac{(x+3)(x+3)}{(3-x)(3+x)}= \frac{a(x-3)}{2(3-x)} [/latex] [latex] \frac{a^{3}+1 }{a-1} : \frac{a^{2}-a+1 }{a^{2}-1}= \frac{(a+1)(a^{2}-a+1) }{a-1}* \frac{(a-1)(a+1)}{a^{2}-a+1} =(a+1)^{2}=a^{2}+2a+1 [/latex]