Question

A student simplified the rational expression using the steps shown. Is the answer correct? Explain.

Option 1: No, the answer is incorrect because the denominator should not contain variables.
Option 2: Yes, the answer is correct as shown.
Option 3: No, the answer is incorrect because the terms in the numerator were not fully factored.
Option 4: Yes, the answer is correct because the terms in the numerator and denominator were properly simplified.

Answer 1

The correct choice is dependent on whether the terms in the numerator were fully factored. Simplification requires factoring to eliminate common factors; Option 3 is correct if the terms were not fully factored.

Step-by-step explanation:

The student's question pertains to the correct simplification of a rational expression. In mathematics, simplification can involve factoring and canceling out common terms between the numerator and denominator. Option 3 is correct if the terms in the numerator were not fully factored, as proper simplification of a rational expression requires factoring to see if common factors can be eliminated. Option 1 is incorrect because rational expressions can have variables in the denominator. Option 4 would be correct only if the simplification was indeed properly done, which includes full factoring and canceling of terms. It is also important to note that while eliminating terms, we must ensure the expression remains an equality. Remember, when multiplying fractions, one should multiply the numerators together, and the denominators together, and simplify by common factors as needed. After simplification, always check if the answer is reasonable.