Question

Am-mb-6a+6b/m^2-36 - сократите дробь

Answer 1

Ответ:

$\frac{am - mb - 6a + 6b}{ {m}^{2} - 36} = \frac{m(a - b) - 6(a - b)}{(m - 6)(m + 6)} = \frac{(a - b)(m - 6)}{(m - 6)(m + 6)} = \frac{a - b}{m + 6}$

Answer 2

To simplify the given expression, we'll first factor the numerator and denominator and then cancel out common terms:

Expression: (am - mb - 6a + 6b) / (m^2 - 36)

Step 1: Factor the numerator: am - mb - 6a + 6b

Factor out 'a' from the first two terms and '6' from the last two terms: a(m - b) - 6(a - b)

Step 2: Factor the denominator: m^2 - 36

Recognize that the denominator is the difference of squares and factor it: (m + 6)(m - 6)

Now the expression becomes: (a(m - b) - 6(a - b)) / ((m + 6)(m - 6))

Step 3: Factor out (m - b) from the numerator: (a - 6)(m - b) / ((m + 6)(m - 6))

Step 4: Cancel out the common term (m - 6) in the numerator and denominator: The simplified expression is: (a - 6) / (m + 6)