simplify the rational expression
3x^2+6x / x^2-16
To simplify the rational expression (3x^2 + 6x) / (x^2 - 16), we can factor the numerator and denominator as much as possible and then cancel any common factors.
Factoring the numerator:
3x^2 + 6x = 3x(x + 2)
Factoring the denominator:
x^2 - 16 = (x + 4)(x - 4)
The rational expression can now be written as:
(3x(x + 2)) / ((x + 4)(x - 4))
Now, we can cancel out common factors.
Removing the common factor of (x + 2) in the numerator and denominator, we get:
(3x) / ((x + 4)(x - 4))
Therefore, the simplified form of the rational expression (3x^2 + 6x) / (x^2 - 16) is:
(3x) / ((x + 4)(x - 4))