section 6.2 adding & subtracting rational expressions
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Section 6.2 Adding & Subtracting Rational Expressions. Adding & Subtracting Rational Expressions with the Same Denominators Finding the LCD of 2 or more Polynomial Denominators Adjusting Opposite Factors in Denominators Adding & Subtracting Rational Expressions - PowerPoint PPT PresentationTRANSCRIPT
6.2 1
Section 6.2 Adding & Subtracting Rational Expressions
Adding & Subtracting Rational Expressions with the Same Denominators
Finding the LCD of 2 or more Polynomial Denominators Adjusting Opposite Factors in Denominators Adding & Subtracting Rational Expressions
with Unlike Denominators 1 1 ? ------------- + -------------- = ----------------
6.2 2
Adding and Subtracting Fractions with Identical Denominators
Perform the operation:
6.2 3
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.
28z3 = (22) (7)(z3) 321z = (3)(7) (z) 4z2
LCD= (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↑
33
2
2
4
4
z
z
)2()2(
aa
)5()5(
aa
6.2 4
? ? ? 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 5
Adjusting an Opposite Denominator Situation: one factor is the opposite of the other For 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 6
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 7
Add & Subtract Practice - monomials
222 21352
7375
212
35
212
xx
xxxx
xx
LacksxLCD
xx
xxx
2
22
)7)(3(
7)3(3
)7)(3(21
Exclusions: x ≠ 0
6.2 8
Add & Subtract Practice - simplifying
2
2
22
2
2
2
2222
2
)(22
)()(2
)(
))(()(2
)(22
2
yxyxx
yxyx
yxx
yxyxyx
yxx
yxyx
yxyxx
LacksyxLCD
yxyxyxyxyxyx
2
222
)(
)()(1)(2
6.2 9
Add & Subtract Practice – change both
)1)(6)(1(4
)1)(6)(1(32132
)1)(6)(1()1)(3()1)(12(
653
6712
222
22
yyyyy
yyyyyyy
yyyyyyy
yyy
yyy
LacksyyyLCD
yyyyy
yyyyy
)1)(6)(1(
)1()1)(6(65
)1()6)(1(672
2
Exclusions: y ≠ ±1, 6
6.2 10
Brain Break:
6.2 11
Add & Subtract – opposite monomials
aaaaaa 41
82
81
83
81
83
aLCD 8
Exclusions: a ≠ 0
6.2 12
Add & Subtract – opposite binomials
yxyx
yxy
yxx
xyy
yxx
2735
2)73(1
25
273
25
xyLCD 2
+
6.2 13
Add & Subtract – function simplification
24
)2)(2()2(4
)2)(2(84
)2)(2(21052
)2)(2()2()2(52)(
21
25
)2)(2(2)(
21
25
42)( 2
xxxx
xxx
xxxxx
xxxxxxf
xxxxxxf
xxxxxf
)2)(2(
)2(2)2(2)2)(2(42
xxLCD
xxxxxxx
Exclusions: x ≠ ±2
6.2 14
What Next? 6.3 Complex Fractions
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