Simplify the sum. State any restrictions on the variable. Show your work.
6z+7/z-4 + 7z+9/z-4
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.
To simplify the given sum, we need to combine like terms.
Step 1: Combine the terms with the same variable, which is "z".
We have 6z + 7z = 13z.
Step 2: Combine the constant terms.
We have 7 - 4 = 3.
Therefore, the simplified sum is (13z + 3)/(z - 4).
Restrictions:
To determine the restrictions on the variable, we need to look for any values of "z" that would make the denominator (z - 4) equal to zero. In this case, if z = 4, the denominator would be zero, which is not allowed.
Therefore, the restriction is z ≠ 4.
To simplify the sum (6z + 7)/(z - 4) + (7z + 9)/(z - 4), we need to combine the fractions into a single fraction.
Step 1: Find a common denominator.
The denominators in both fractions are the same, which is (z - 4). So, we don't need to find a common denominator.
Step 2: Combine the numerators.
Add the numerators together to get the numerator of the combined fraction:
(6z + 7) + (7z + 9) = 6z + 7z + 7 + 9 = 13z + 16
Step 3: Combine the fractions.
Place the combined numerator over the common denominator:
(13z + 16)/(z - 4)
There are no restrictions on the variable z, as long as z ≠ 4, because the denominator cannot be zero to avoid division by zero.
Therefore, the simplified sum is (13z + 16)/(z - 4), and the restriction is z ≠ 4.