Add. State the sum in simplest form.
(x^2)/(x+2) + (4x)/(x+2) + (4)/(x+2), x ≠ -2
To add the fractions, we need a common denominator. In this case, the common denominator is (x+2).
The fractions can be rewritten as follows:
(x^2)/(x+2) + (4x)/(x+2) + (4)/(x+2) = (x^2 + 4x + 4)/(x+2)
The numerator can be simplified by factoring:
(x^2 + 4x + 4) = (x + 2)(x + 2) = (x + 2)^2
Thus, the sum of the fractions in simplest form is (x + 2)^2/(x+2).
However, for x ≠ -2, we need to exclude x = -2 from the domain.
Add. State the sum in simplest form.
(x^2)/(x+2) + (4x)/(x+2) + (4)/(x+2), x ≠ -2
The sum of the fractions is:
(x^2 + 4x + 4)/(x+2).
However, for x ≠ -2, we need to exclude x = -2 from the domain, as stated in the question.
Add. State the sum in simplest form.
(x^2)/(x+2) + (4x)/(x+2) + (4)/(x+2), x ≠ -2
A. x + 2
B. x + 4
C. (x^2 + 4x + 4)/(x^3 + 8)
D. x^2 + 2x + 2
The sum of the fractions is:
(x^2 + 4x + 4)/(x+2).
We can simplify the numerator by factoring:
(x^2 + 4x + 4) = (x + 2)(x + 2) = (x + 2)^2.
Therefore, the sum in simplest form is:
(x + 2)^2/(x+2).
However, since x ≠ -2, we can cancel out the common factor of (x + 2):
(x + 2)^2/(x+2) = x + 2.
Hence, the simplified sum is x + 2, so the correct answer is A. x + 2.