Question

1. Сократить дробь frac{3m^{2}-2mn-n^{2}}{6m^{2}-7mn+n^{2}}

Answer 1

$frac{3m^2-2mn-n^2}{6m^2-7mn+n^2}= frac{2m^2+m^2-2mn-n^2}{6m^2-6mn-mn+n^2}= frac{(2m^2-2mn)+(m^2-n^2)}{(6m^2-6mn)-(mn-n^2)}=\=frac{2m(m-n)+(m-n)(m+n)}{6m(m-n)-n(m-n)}= frac{(m-n)(2m+m+n)}{(m-n)(6m-n)}= frac{3m+n}{6m-n}$