Question

Сократить дробь(2m^2-3m-14)/(4m^2-49)​

Answer 1

$\frac{2m^2-3m-14}{4m^2-49}=\frac{2(m+2)(m-\frac{7}{2})}{(2m-7)(2m+7)}=\frac{(m+2)(2m-7)}{(2m-7)(2m+7)}=\frac{m+2}{2m+7}\\\\\\2m^2-3m-14=0\; \; ,\; \; D=121\; ,\; \; m_1=-2\; ,\; m_2=\frac{7}{2}$

Answer 2

Объяснение:

(2m²-3m-14)/(4m²-49) - распишем скобки и числителя, и знаменателя по формуле a²-b²:

2m²+4m-7m-14/(2m-7)(2m+7) - вынесем общий множитель, чтобы было что сокращать:

2m(m+2)-7(m+2)/(2m-7)(2m+7) - преобразовали еще один общий множитель m+2, - выносим его тоже:

(2m-7)(m+2)/(2m-7)(2m+7) - сокращаем (2m-7):

m+2/2m+7 - ответ.

Answer 3

To simplify the fraction (2m^2 - 3m - 14) / (4m^2 - 49), we can first factor both the numerator and the denominator, and then cancel out any common factors.

1. Factor the numerator (2m^2 - 3m - 14): The numerator can be factored as follows: 2m^2 - 3m - 14 = (2m + 7)(m - 2)

2. Factor the denominator (4m^2 - 49): The denominator is the difference of squares, and it can be factored as follows: 4m^2 - 49 = (2m + 7)(2m - 7)

Now, the fraction becomes: (2m + 7)(m - 2) / (2m + 7)(2m - 7)

3. Cancel out common factors: We can see that (2m + 7) is a common factor in both the numerator and the denominator, so it can be canceled out. The simplified fraction is: (m - 2) / (2m - 7)

So, the simplified form of the fraction is (m - 2) / (2m - 7).