Section 6.2 Adding & Subtracting

Section 6.2 Adding & Subtracting - PPT

Rational Expressions. Adding & Subtracting . Rational Expressions . with the Same Denominators. Finding the LCD of 2 or more Polynomial Denominators. Adjusting . Opposite Factors . in Denominators. ID: 476866

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Section 6.2 Adding & Subtracting

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Section 6.2 Adding & Subtracting
Rational Expressions
Adding & Subtracting
Rational Expressions
with the Same DenominatorsFinding the LCD of 2 or more Polynomial DenominatorsAdjusting Opposite Factors in DenominatorsAdding & Subtracting Rational Expressions with Unlike Denominators 1 1 ? ------------- + -------------- = ----------------
6.2
1
Adding and Subtracting Fractions with Identical Denominators
Perform the operation
:
6.2
2
Finding the LCD (must be done before adding or subtracting 2 or more RE’s)
1. Factor each denominator completely into primes.2. List all factors of each denominator. (use powers when duplicate factors exist)3. The LCD is the product of each factor to its highest power.
28z
3
= (2
2
) (7)(z3) 321z = (3)(7) (z) 4z2LCD= (22)(3)(7)(z3) Lacks↑
(a2 – 25) = (a + 5)(a – 5) (a + 2)(a + 7a + 10) = (a + 5) (a + 2) (a – 5) LCD = (a + 5)(a – 5)(a + 2) Lacks↑
6.2
3
? ? ? 8(x – 3) (x2 – x – 6) (2x2 – 12x + 18) 8(x – 3) = (2)3(x – 3) (x + 2)(x – 3) (x2 – x – 6) = (x – 3)(x + 2) 8(x – 3)(2x2 – 12x + 18) = (2) (x – 3)2 4(x + 2) LCD = (2)3 (x – 3)2(x + 2) Lacks↑
Find the LCD, using a Primes Table
6.2
4
Adjusting an Opposite Denominator
Situation: one factor is the opposite of the otherFor 7 and 2 find the LCD 3(a – 2) (2 – a)For the second expression, multiply top and bottom by -1 (doesn’t change its value)Now 7 and -2 find the LCD 3(a – 2) (a – 2)Do this after factoring, before writing the LCD
6.2
5
1.
Find the LCD.2. Express each rational expression with a denominator that is the LCD.3. Add (or subtract) the resulting rational expressions.4. Simplify the result if possible.
Adding or subtracting rational expressions with unlike denominators – note any exclusions
Exclusions:
a ≠ ±2
6.2
6
Add & Subtract Practice - monomials
Exclusions:
x ≠ 0
6.2
7
Add & Subtract Practice - simplifying
6.2
8
Add & Subtract Practice – change both
Exclusions:
y ≠ ±1, 6
6.2
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0
Brain Break:
6.2
10
1
Add & Subtract – opposite monomials
Exclusions:
a ≠ 0
6.2
11
2
Add & Subtract – opposite binomials
+
6.2
12
3
Add & Subtract – function simplification
Exclusions:
x ≠ ±2
6.2
13
4
What Next?
6.3 Complex Fractionsnext time
6.2
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5
6
7