P.6 SYMKC Rational Expressions Vocabulary, Formulas, Concepts

Question 1

ratio of two polynomials in which the denominator is not the zero polynomial (denominator cannot be 0)

Answer 1

Rational Expression

Question 2

the set of all numbers that can be used in place of the variable

Answer 2

domain of a rational expression

Question 3

How do you find the domain of a rational expression

Answer 3

Set the denominator equal to zero and solve. Write the answer in interval notation with these values excluded.

Question 4

How do you reduce rational expressions

Answer 4

Factor the numerator and denominator completely.
Divide (cancel out) the common factors.

Question 5

How do you multiply rational expressions

Answer 5

Factor out all numerators and denominators completely. Cancel out all common factors diagonally and vertically. Never horizontally. Multiply together the remaining factors after cancellation in factored form.

Question 6

How do you divide rational expressions

Answer 6

Change the problem to multiplication by making the second fraction its reciprocal. Factor out all numerators and denominators completely. Cancel out all common factors diagonally and vertically. Never horizontally. Multiply together the remaining factors after cancellation in factored form.

Question 7

items in the domain that would make the rational expression undefined

Answer 7

excluded values

Question 8

When adding and subtracting rational expressions, you must have a ___________.

Answer 8

common denominator

Question 9

How do you find a common denominator of a rational expression

Answer 9

Factor out each denominator. Compare. Multiply the fractions (numerator and denominator) by what is required to make the denominators the same.

Question 10

After finding a common denominator in an addition or subtraction problem, what do you do next?

Answer 10

Add/subtract the numerators. The denominators stay the same. After adding and subtracting, factor the numerator again to see if you can cancel a common factor with the denominator.

Question 11

the smallest number that is a multiple of all denominators

Answer 11

Least common denominator (LCD)

Question 12

How do you find an LCD

Answer 12

Factor each denominator completely.
Write a product using each factor that appears in the denominator.
For each factor, use the highest power of that factor that occurs in the denominators.

Question 13

a fraction having rational expressions in the numerator, denominator, or both (Fractions over fractions)

Answer 13

complex fractions