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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) 3
21z = (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↑
3
3
2
2
4
4
z
z
)2(
)2(
a
a
)5(
)5(
a
a
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 21
352
73
75
21
2
3
5
21
2
x
x
xxx
x
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
yx
yxx
yx
yx
yx
x
yxyx
yx
yx
x
yx
yx
yxyx
x
LacksyxLCD
yxyxyx
yxyxyx
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(
65
3
67
12
222
22
yyy
yy
yyy
yyyy
yyy
yyyy
yy
y
yy
y
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 4
1
8
2
8
1
8
3
8
1
8
3
aLCD 8
Exclusions: a ≠ 0
6.2 12
Add & Subtract – opposite binomials
yx
yx
yx
y
yx
x
xy
y
yx
x
2
735
2
)73(1
2
5
2
73
2
5
xyLCD 2
+
6.2 13
Add & Subtract – function simplification
2
4
)2)(2(
)2(4
)2)(2(
84
)2)(2(
21052
)2)(2(
)2()2(52)(
2
1
2
5
)2)(2(
2)(
2
1
2
5
4
2)(
2
xxx
x
xx
x
xx
xxx
xx
xxxxf
xxxx
xxf
xxx
xxf
)2)(2(
)2(2
)2(2
)2)(2(42
xxLCD
xx
xx
xxx
Exclusions: x ≠ ±2
6.2 14
What Next? 6.3 Complex Fractions
next time
