Marissa was asked to make an equivalent form of the rational expression, -3x^2 - 15x - 18/x+3. which of the following is a correct equivalent form?
-3x - 114
-3x - 24 - 114/x+3
-3x - 6
This rational expression does not have any equivalent forms
The correct equivalent form of the given rational expression, -3x^2 - 15x - 18/(x+3), is -3x - 6.
To make an equivalent form of the given rational expression, -3x^2 - 15x - 18/x+3, we can start by factoring the numerator, -3x^2 - 15x - 18. The numerator can be factored as follows:
-3x^2 - 15x - 18 = -3(x^2 + 5x + 6)
= -3(x + 3)(x + 2)
So, the factored form of the numerator is -3(x + 3)(x + 2).
Now, the equivalent form of the given rational expression is:
-3(x + 3)(x + 2)/(x + 3)
To simplify this expression, we can cancel out the common factor of (x + 3):
-3(x + 2)
Therefore, the correct equivalent form of the rational expression is -3(x + 2). Among the given options, the correct equivalent form is -3x - 6.
To find an equivalent form of the given rational expression, we need to simplify it by factoring if possible and cancel out any common factors.
The given rational expression is: -3x^2 - 15x - 18 / (x + 3).
First, let's factor the numerator:
-3x^2 - 15x - 18 = -3(x^2 + 5x + 6)
Now, let's factor the quadratic expression inside the parentheses:
x^2 + 5x + 6 = (x + 2)(x + 3)
So, the factored form of the numerator is -3(x + 2)(x + 3).
Now, let's cancel out the common factor of (x + 3) in the numerator and denominator:
-3(x + 2)(x + 3) / (x + 3) = -3(x + 2)
The correct equivalent form of the given rational expression is -3(x + 2).
Therefore, the correct answer among the options is: -3x - 6.