Question

4m^2-9n^2
-------------------------- =
9n^2-12mn+4m^2

Answer 1

Ответ:

$\dfrac{2m+3n}{2m-3n}$

Объяснение:

$\dfrac{4m^{2}-9n^{2}}{9n^{2}-12mn+4m^{2}}=\dfrac{2^{2}m^{2}-3^{2}n^{2}}{3^{2}n^{2}-12mn+2^{2}m^{2}}=\dfrac{(2m)^{2}-(3n)^{2}}{(3n)^{2}-2 \cdot 3n \cdot 2m+(2m)^{2}}=$

$=\dfrac{(2m-3n)(2m+3n)}{(3n-2m)^{2}}=\dfrac{(2m-3n)(2m+3n)}{(2m-3n)^{2}}=\dfrac{2m+3n}{2m-3n};$