Simplify the sum. State any restrictions on the variable.
2x+2/x-3 + 2x+5/x-3
The simplified sum is:
(2x + 2 + 2x + 5) / (x - 3)
Combining like terms in the numerator, we have:
(4x + 7) / (x - 3)
There are no restrictions on the variable x.
To simplify the sum, we combine the two fractions by finding a common denominator. In this case, the common denominator is (x - 3):
(2x + 2)/(x - 3) + (2x + 5)/(x - 3)
Now, we can add the numerators together:
(2x + 2 + 2x + 5)/(x - 3)
Simplifying the numerator:
(4x + 7)/(x - 3)
Therefore, the simplified sum is (4x + 7)/(x - 3).
As for restrictions on the variable, we need to remember that the denominator (x - 3) cannot equal 0, as division by zero is undefined. Therefore, the restriction on the variable is x ≠ 3.
To simplify the given sum, we need to combine the fractions by finding a common denominator. In this case, the common denominator is (x - 3).
Let's apply the common denominator to each fraction:
= (2x + 2) / (x - 3) + (2x + 5) / (x - 3)
Now, we can combine the fractions by adding their numerators:
= (2x + 2 + 2x + 5) / (x - 3)
Combining like terms in the numerator:
= (4x + 7) / (x - 3)
This is the simplified form of the given sum.
Now, let's consider any restrictions on the variable (x). In this case, the only restriction is that x cannot be equal to 3 since it would result in division by zero. Hence, the restriction is x ≠ 3.