Question

27m^6+n^6/n^2-9m^2: (3m^2-n^2)^2+3m^2n^2/3m-n

Answer 1

$\frac{27 {m}^{6} + {n}^{6} }{ {n}^{2} - 9 {m}^{2} } \div \frac{(3 {m}^{2} - {n}^{2} ) ^{2} + 3 {m}^{2} {n}^{2} }{3m - n} = \frac{(3 {m}^{2} + {n}^{2} )(9 {m}^{4} - 3 {m}^{2} {n}^{2} + {n}^{4} ) }{(n - 3m)(n + 3m)} \times \frac{3m - n}{9 {m}^{4} - 6 {m}^{2} {n}^{2} + {n}^{4} + 3 {m}^{2} {n}^{2} } = \frac{(3 {m}^{2} + {n}^{2} )(9 {m}^{4} - 3 {m}^{2} {n}^{2} + {n}^{4} )}{(n - 3m)(n + 3m)} \times \frac{ - (n - 3m)}{9 {m}^{4} - 3 {m}^{2} {n}^{2} + {n}^{4} } = \frac{ - ( 3{m}^{2} + {n}^{2}) }{n + 3m}$

Answer 2