Multiplying and Dividing Rational Expressions — Quiz

Question 4 • Algebra: Concepts and Connections

Which expression will simplify to 1 ? Assume m is not equal to 9 and m is not equal to negative 9

Answer

open paren the fraction with numerator m plus 9 and denominator m minus 9 close paren times open paren the fraction with numerator 9 plus m and denominator 9 minus m close paren

open paren the fraction with numerator m plus 9 and denominator m minus 9 close paren times open paren the fraction with numerator m minus 9 and denominator m plus 9 close paren

open paren the fraction with numerator m plus 9 and denominator m minus 9 close paren times open paren the fraction with numerator m plus 9 and denominator m minus 9 close paren

open paren the fraction with numerator m plus 9 and denominator m minus 9 close paren times open paren the fraction with numerator 9 minus m and denominator 9 plus m close paren

Explanation

In choice B, the second fraction is the reciprocal of the first: (m − 9)/(m + 9) reverses the numerator and denominator of (m + 9)/(m − 9). A nonzero expression multiplied by its reciprocal equals 1. The assumptions m ≠ 9 and m ≠ −9 ensure the denominators are not zero.

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