Question

Сократите дробь: m^2-n2-km+kn/k^2-km-mn-n^2 вычислите: 6^-5/27^-2*4^-4

Answer 1

$\frac{m^2-n^2-km+kn}{k^2-km-mn-n^2}=\frac{(m^2-n^2)-(km-kn)}{(k^2-n^2)-(km+mn)}= \frac{(m-n)(m+n)-k(m-n)}{(k-n)(k+n)-m(k+n)}= \\ =\frac{(m-n)(m+n-k)}{(k+n)(k-n-m)}=\frac{-(m-n)(k-m-n)}{(k+n)(k-n-m)}= \frac{-(m-n)}{k+n}= \frac{n-m}{k+n} \\ \frac{6^{-5}}{27^{-2}*4^{-4}}= \frac{2^{-5}*3^{-5}}{3^{-6}*2^{-8}}=2^{-5-(-8)}*3^{-5-(-6)}=2^3*3^1=24$