Final answer:
The student's question involves rationalizing the denominator in algebraic expressions, a process that simplifies the expressions by eliminating radicals or irrational numbers in the denominator and often makes further algebraic operations more straightforward.
Step-by-step explanation:
Rationalizing the Denominator
The student's question relates to the process of rationalizing the denominator when dealing with algebraic expressions, particularly involving fractions and radicals. To rationalize the denominator, you usually multiply the numerator and denominator by a term that will eliminate the radical or irrational number in the denominator. When units cancel out properly during this process, simplifying the algebraic expression becomes easier.
For example, when you have a fraction such as 1/√2, you would multiply both the numerator and the denominator by √2 to get √2/2 as the rationalized fraction. Here, you are simply multiplying the numerators together and doing the same with the denominators, which can sometimes involve division of exponentials. This means dividing the digit terms and subtracting the exponents when the bases are the same.
After simplifying, it is important to eliminate terms wherever possible to simplify the algebra further and check the answer to ensure it is reasonable. This process of rationalization is important as it often makes subsequent algebraic operations easier and is required to arrive at a standard form for answers in mathematics.