Question

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

Answer 1

Ответ:

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

Объяснение:

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

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

Answer 2

To simplify the expression (4m^2 - 9n^2) / (9n^2 - 12mn + 4m^2), we can factor the numerator and the denominator to see if any common factors can be canceled out:

Numerator (4m^2 - 9n^2): This is a difference of squares and can be factored as (2m - 3n)(2m + 3n).

Denominator (9n^2 - 12mn + 4m^2): This is a trinomial and can be factored as (3n - 2m)(3n - 2m).

Now, the expression becomes:

[(2m - 3n)(2m + 3n)] / [(3n - 2m)(3n - 2m)]

Since the denominator factors are the same, we can simplify further:

(2m - 3n)(2m + 3n) / [(3n - 2m)^2]

So, the simplified expression is:

(2m - 3n)(2m + 3n) / (3n - 2m)^2