Final answer:
The equivalent expression in lowest terms of 2x + 4x / (x² + 5x + 6) is 6x / (x + 2)(x + 3), as the numerator and denominator do not share common factors.
Step-by-step explanation:
The student has asked what the equivalent expression in lowest terms of the algebraic expression 2x + 4x / (x² + 5x + 6) is. To simplify this expression, we must first recognize that the numerator can be combined because they are like terms. Doing so gives us 6x as the new numerator. Next, we need to factor the denominator, if possible, to see if it can be simplified with the numerator. The quadratic x² + 5x + 6 factors into (x + 2)(x + 3). However, the numerator 6x does not contain a factor that is common with the denominator, so the expression cannot be simplified any further. Therefore, the equivalent expression in lowest terms is 6x / (x + 2)(x + 3).