Final answer:
To simplify (x²+2x)/(2x+4), factor out the greatest common factor from both the numerator and the denominator, then cancel the common factor to get the reduced expression x/2.
Step-by-step explanation:
The student asked how to reduce the rational expression (x²+2x)/(2x+4) to its lowest terms. To simplify this expression, we first factor out the greatest common factor in the numerator, which is x. This gives us x(x+2). The denominator 2x+4 can also be factored as 2(x+2). The expression is simplified by canceling out the common factor (x+2) from the numerator and the denominator, leaving us with the simplified expression x/2. So, the reduced form of the rational expression (x²+2x)/(2x+4) is x/2.