Question

m^(-6)-27*27 *m^2. 9m^2(1+3m)
_____________________+ _________
(9-6/m+1/m^2)(9+3/m+1/m^2). (3m-1)


Ответ:3m+1

Answer 1

$frac{( m^{-6} -27*27)*m^2}{(9- frac{6}{m}+ frac{1}{m^2} )(9+ frac{3}{m} + frac{1}{m^2} ) } + frac{9m^2(1+3m)}{3m-1} = \ \ frac{ frac{1}{m^4}-(27m)^2 }{ frac{9m^2-6m+1}{m^2}* frac{9m^2+3m+1}{m^2} } +frac{9m^2(1+3m)}{3m-1} = \ \ frac{( frac{1}{m^2}-27m)( frac{1}{m^2}+27m) }{ frac{(3m-1)^2(9m^2+3m+1)}{m^4} } +frac{9m^2(1+3m)}{3m-1} = \ \ frac{ frac{(1-27m^3)(1+27m^3)}{m^4} }{ frac{(3m-1)^2(9m^2+3m+1)}{m^4} } +frac{9m^2(1+3m)}{3m-1} =$
$frac{(1-3m)(1+3m+9m^2)(1+3m)(1-3m+9m^2)}{(3m-1)^2(9m^2+3m+1)} +frac{9m^2(1+3m)}{3m-1} = \ \ frac{-(1+3m)(1-3m+9m^2)}{3m-1} +frac{9m^2(1+3m)}{3m-1} = \ \ frac{(1+3m)(9m^2-1+3m-9m^2)}{3m-1} = frac{(1+3m)(3m-1)}{3m-1} =3m+1$