Question

M²-n²/(m-n)²: 3(m n)/ 2( m-n)

Answer 1

$\frac{m^2-n^2}{(m-n)^2} : \frac{3(m+n)}{2(m-n)}= \frac{(m-n)(m+n)}{(m-n)^2} * \frac{2(m-n)}{3(m+n)}= \frac{2}{3}$

Answer 2

To simplify the expression (M² - N²) / (M - N)², we can factorize the numerator and denominator.

First, let's factorize the numerator using the difference of squares identity:

M² - N² = (M + N)(M - N)

Now, let's factorize the denominator:

(M - N)² = (M - N)(M - N)

The expression becomes:

(M + N)(M - N) / (M - N)(M - N)

Next, we can cancel out the common factor of (M - N) in the numerator and denominator:

(M + N) / (M - N)

Therefore, the simplified expression is (M + N) / (M - N).

Now, let's simplify the expression 3(MN) / 2(M - N):

First, distribute the factor of 3 to both terms in the numerator:

3MN / 2(M - N)

Finally, there are no common factors to cancel out, so the expression remains as:

3MN / 2(M - N)

Therefore, the simplified expression is 3MN / 2(M - N).