Vocabulary
A ______ is a ratio of two polynomials.
rational expression
(x² + 10x + 25) / (x² + 9x + 20)
(x + 5) / (x + 4)
(8y - 4) / (10y - 5) * (5y - 15) / (3y - 9)
4/3
(x² + 10x + 25) / (x² + 9x + 20)
D: xne-4,-5
(8y - 4) / (10y - 5) * (5y - 15) / (3y - 9)
D: yne3, 1/2
An ______ is a value or set of values for x which results in a denominator of 0
domain restriction or excluded value
(x² - 6x - 16) / (x² + 5x + 6)
(x - 8) / (x + 3)
(2x + 12) / (3x - 9) * (2x - 6) / (3x + 8)
(4(x + 6)) / (3(3x + 8))
(x² - 6x - 16) / (x² + 5x + 6)
D: xne-2,-3
(2x + 12) / (3x - 9) * (2x - 6) / (3x + 8)
D: xne3, -8/3
To simplify a rational expression, you must first ______ .
factor it
(6c² + 9c) / (3c)
2c + 3
(x² - 4) / (x² - 1) * (x + 1) / (x² + 2x)
(x - 2) /(x(x - 1))
(6c² + 9c) / (3c)
D: cne0
(x² - 4) / (x² - 1) * (x + 1) / (x² + 2x)
D: xne1, -1, -2, 0
A binomial that factors into binomial conjugates such as (x+5)(x-5) is called ______.
a difference of squares
(2x² - 3x - 2) / (x² - 5x + 6)
(2x + 1) / (x - 3)
(6x + 6y) / (x - y) -: 18 / (5x - 5y)
(5(x + y) )/ 3
(2x² - 3x - 2) / (x² - 5x + 6)
D: xne2,3
(6x + 6y) / (x - y) -: 18 / (5x - 5y)
D: xney
Factor the ______ of the rational expression in order to find the domain restrictions.
denominator
(x² + 8x + 16) / (x² - 2x - 24)
(x + 4) / (x - 6)
(3y - 12) / (2y + 4) -: (6y - 24) / (4y + 8)
1
(x² + 8x + 16) / (x² - 2x - 24)
D: xne-4,6
(3y - 12) / (2y + 4) -: (6y - 24) / (4y + 8)
D: yne-2, 4