Rationalizing Denominators (1.6.3)

Question 1

Fractions

Answer 1

The number 1 can be written as a fraction with any number or expression as the numerator so long as the same number or expression is used as the denominator (except for 0). In other words, 1 = 78/78 or (3a + b)/(3a + b), and so on.

Question 2

Clearing a Denominator

Answer 2

Clearing a denominator of radicals means to multiply the fraction by a version of 1. Your version of 1 will be the radical over itself. So, the denominator multiplies out the radical to clear it, and the numerator gets a radical. This process is called rationalizing the denominator.

Question 3

Conjugate

Answer 3

The conjugate of a given binomial is a binomial that contains the same terms but with the opposite sign connecting the two terms; i.e., (a – b) and (a + b) are conjugates of each other. When you multiply a binomial by its conjugate, you are left with the difference of two squares and no middle terms.

Question 4

FOIL

Answer 4

First terms.
Outer terms.
Inside terms.
Last terms, and combining like terms.