Which expression is equivalent to the base of the original expression (1 - x/(x+blah))^20 before raising to the 20th power?

• A. x/(x+blah)
• B. blah/(x+blah)
• C. (x+blah - x)/(x+blah)
• D. blah/(x+blah)^2

Answer: (B)

Combining fractions to simplify shows the base 1 minus x over (x plus blah) can be rewritten with a common denominator. Write 1 as (x+blah)/(x+blah), then subtract x/(x+blah) to get (x+blah)/(x+blah) - x/(x+blah) = (x+blah - x)/(x+blah) = blah/(x+blah). So the base before raising to the 20th power is blah/(x+blah), the simplest form. The other forms either drop the subtraction, or change the denominator, so they don’t match the base as cleanly, while one could also express it as (x+blah - x)/(x+blah), which is algebraically the same but not the most streamlined form.