Question
Simplify the sum. State any restrictions on the variable. Show your work.
6z+7/z-4 + 7z+9/z-4
6z+7/z-4 + 7z+9/z-4
Answers
GPT 3.5
To simplify the sum, we need to combine the fractions with the same denominator.
(6z+7)/(z-4) + (7z+9)/(z-4)
Since the denominators are the same, we can combine the numerators:
(6z + 7 + 7z + 9)/(z - 4)
Now, we can combine the like terms in the numerator:
(13z + 16)/(z - 4)
Therefore, the simplified sum is (13z + 16)/(z - 4).
Restrictions on the variable:
The variable 'z' cannot be equal to 4 because it would result in a division by zero, which is undefined. So, z ≠ 4.
(6z+7)/(z-4) + (7z+9)/(z-4)
Since the denominators are the same, we can combine the numerators:
(6z + 7 + 7z + 9)/(z - 4)
Now, we can combine the like terms in the numerator:
(13z + 16)/(z - 4)
Therefore, the simplified sum is (13z + 16)/(z - 4).
Restrictions on the variable:
The variable 'z' cannot be equal to 4 because it would result in a division by zero, which is undefined. So, z ≠ 4.