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[latex] \frac{c^2-10c+25}{c^2+3c+9} : \frac{6c^2-30c}{c^3-27}- \frac{c-2}{6} = \frac{c^2-2*c*5+5^2}{c^2+3c+9} * \frac{c^3-3^3}{6c*c-6c*5}- \frac{c-2}{6} =[/latex] [latex]= \frac{(c-5)^2}{c^2+3c+9} * \frac{(c-3)(c^2+3c+9)}{6c*(c-5)}- \frac{c-2}{6} =[/latex] [latex]= \frac{(c-5)*(c-5)(c^2+3c+9)*(c-3)}{6c*(c-5)(c^2+3c+9)}- \frac{c-2}{6} = \frac{(c-5)*(c-3)}{6c}- \frac{c-2}{6} =[/latex] [latex]= \frac{(c-5)*(c-3)}{6*c}- \frac{(c-2)*c}{6*c} = \frac{(c-5)*(c-3)-c*(c-2)}{6*c} =[/latex] [latex]=\frac{c^2-3c-5c+15-c^2+2c}{6c} = \frac{-6c+15}{6c} = -\frac{3*2c-3*5}{3*2c}= \frac{3*(2c-5)}{3*2c}=\frac{2c-5}{2c}=[/latex] [latex]= \frac{2c}{2c} - \frac{5}{2c} =1- \frac{5}{2c} [/latex]