A.4 Rational Expressions

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Presentation transcript:

A.4 Rational Expressions Domain: the set of x-values. The domain of a polynomial is always all Real numbers except for two cases: 1. Denominators 2. Radicals

Determine the domain of each of the following: a. 3x3 + 4x +7 Is there a den. or radical in it? is the domain. To find the domain with a radical, set the inside b. is the domain

c. Since this example has a denominator in it, what x-value will make it undefined? The domain will be all real numbers except…. x - 3 = 0 or x = 3 The answer will look like this...

Ex. 2 Reducing a rational expression.

Ex. 3 a. b.

Ex. 4 Multiplying Rational Expressions

Ex. 5 Dividing Rational Expressions Now factor everything. Day 1

Ex. 6 Subtracting Rational Expressions Dist.

Ex. 7 (x-1)(x+1)

Ex. 8 Compound Fractions x - 2 Get common den.’s for N & D Now, invert the den. and mult.

Ex. 9 Simplifying a Compound Fraction by Multiplying by the LCD. What is the LCD of all four denominators? Now, mult. both the top and bottom by x2y2

Ex. 10 Simplifying with Negative Exponents Factor out the smallest exponent possible. -3/2 is less than -1/2 so we will use -3/2

Ex. 11 Simplify the expression by rationalizing the numerator. 1