Question
Simplify the sum. State any restrictions on the variable. Show your work.
2x+2/x-3 + 2x+5/x-3
2x+2/x-3 + 2x+5/x-3
Answers
GPT 3.5
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.
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.