Simplify the sum. State any restrictions on the variable. Show your work.
2x+2/x-3 + 2x+5/x-3
To simplify the sum, we can combine the two fractions by finding a common denominator.
The common denominator in this case is (x - 3). So, we can rewrite the expression as:
(2x + 2)/(x - 3) + (2x + 5)/(x - 3)
Now, let's combine the two fractions:
(2x + 2 + 2x + 5)/(x - 3)
Combining like terms in the numerator, we get:
(4x + 7)/(x - 3)
Therefore, the simplified sum is (4x + 7)/(x - 3). The restriction on the variable is x cannot be equal to 3, as it would make the denominator zero.
To simplify the sum (2x + 2) / (x - 3) + (2x + 5) / (x - 3), we first need to find a common denominator for the fractions. Since both denominators are the same (x - 3), we can combine the numerators over the common denominator.
(2x + 2 + 2x + 5) / (x - 3)
Now, we can simplify the numerator by combining like terms:
(4x + 7) / (x - 3)
Therefore, the simplified sum is (4x + 7) / (x - 3).
As for the restrictions on the variable, since we have a denominator of (x - 3), the variable x cannot be equal to 3, as it would result in division by zero. Thus, the restriction is x ≠ 3.
To simplify the sum (2x + 2)/(x - 3) + (2x + 5)/(x - 3), we can combine the two fraction terms with a common denominator.
Step 1: Find the common denominator
The common denominator is (x - 3), as both fractions have the same denominator.
Step 2: Combine the numerators
Add the numerators (2x + 2) and (2x + 5) together:
(2x + 2) + (2x + 5) = 4x + 7
Step 3: Write the combined numerator over the common denominator
The sum of the numerators is 4x + 7. Thus, the simplified expression is:
(4x + 7)/(x - 3)
Restrictions on the variable:
The variable x cannot equal 3, as it would result in a denominator of zero, which is undefined. So the restriction on the variable is x ≠ 3.