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6.2 – Rational ExpressionsAdding and Subtracting
6
5
3
2and
What is the Lowest Common Denominator (LCD)?
2
1
7
2,
4
3and
3 5
5 13and
x x4 2
17 3
4 6and
y y
6 28
5x 12 4y
5
7
5
3
a
aand
a
a
What is the Lowest Common Denominator (LCD)?
123
5
4
72
2
x
xand
x
x
5a
3
27xand 5x
4x 4x
243 x
4x 4x 3 4x 5a
6.2 – Rational ExpressionsAdding and Subtracting
23
3
32
522
yy
yand
yy
y
What is the Lowest Common Denominator (LCD)?
1y
5y
3y 2y
3y 1y and
3y
1y 2y
6.2 – Rational Expressions – Add. And Sub.
73
7
73
3
xx
x
Examples (Like Denominators):
1
3 7x 3x 7
6.2 – Rational Expressions – Add. And Sub.
2
64
2
52 2
x
x
x
xx
Examples (Like Denominators):
2x 22 5
2
x x
x
22
2
x
x
2x
32 x22 5x x 4 6x
4x 6
x 6
2x 2 3x
6.2 – Rational Expressions – Add. And Sub.
65
72
65
1322
xx
x
xx
x
Examples (Like Denominators):
65
72132
xx
xx
65
132
xx
x x2 7
65
62
xx
x
6x
x 1 x 6
1
1
x
1
1
6.2 – Rational Expressions – Add. And Sub.
Examples:
15
3
5
yy
LCD 15
15
3
5
yy
3
3
15
3
15
3 yy
15
33 yy 15
00
6.2 – Rational Expressions – Add. And Sub.
Examples:
210
11
8
5
xx
LCD 40x2
210
11
8
5
xx
x
x
5
5
22 40
44
40
25
xx
x
240
1125
x
x
4
4
6.2 – Rational Expressions – Add. And Sub.
Examples:
1
2
7
5
xx
LCD
5 2
7 1x x
7 1 7 1x x x x
7 1x x
7x 1x
1
1
x
x
7
7
x
x
5x 5 14x 19x 5
6.2 – Rational Expressions – Add. And Sub.
3
5
9
102
xx
xExamples:
10x
10 5
3 3 3
x
x x x
10
3 3
x
x x
3 3x x
3 3x x
3 3x x
3
5
x
3x 3x
LCD
3
3
x
x
3 3x x 5x 15
10x 155x
5x 15
5 3x 3x 3x
5
3x
6.2 – Rational Expressions – Add. And Sub.
812
3
23
42
x
x
xx
Examples:
LCD
4
4 3
3 2 4 3 2
x
x x x
x 3 2x 3x
4 3 2x
4 x 3 2x
4
4
x
x
6.2 – Rational Expressions – Add. And Sub.
Examples: continued
4 3 2 4 3 2x x x x
4 3 2x x
x
x
x
x
xx 234
3
23
4
4
4
16 23x
216 3x
6.2 – Rational Expressions – Add. And Sub.
444
622
x
x
xx
xExamples:
6x x
LCD
6
2 2 2 2
x x
x x x x
2x 2x 2x 2x
2x 2x 2x
2
2
x
x
2
2
x
x
6.2 – Rational Expressions – Add. And Sub.
Examples: continued
2
2
2222
6
2
2
x
x
xx
x
xx
x
x
x
2 2 2 2 2 2x x x x x x
222
2126 22
xxx
xxxx
2 2 2x x x 22 2x x
26x 12x2x 2x
27x 10x x 7x 10
6.2 – Rational Expressions – Add. And Sub.
Defn: A rational expression whose numerator, denominator, or both contain one or more rational expressions.
7
5
yx
xyyx
873
4 3
1
1
xx
x
6.3 – Simplifying Complex FractionsComplex Fractions
3 24 31 32 8
3 24 31 32 8
3 43 4
4
3 24 3
1 384 2
24 24
2
3 24 31
43
2 824
9 812 12
4 38 8
6 3 8 2
12 1 3 3
11278
18 16
12 9
2
212
21
LCD: 12, 8 LCD: 24
6.3 – Simplifying Complex Fractions
24
8
7
12
1
7
8
12
12
3
24
LCD: y
1
2 1
xy
xy
1
2 1
y y
y
xy
xy
2 1
y x
x
yx
yx
12
1y–y
6.3 – Simplifying Complex Fractions
LCD: 6xy
56
3
yy xyx
2
2 2
5 6
2 6
x y
xy x y
56
3
6 6
6 6
yy x
xy xy
yy
xx xy
25 6x y2xy 3y x
xy
xy
y
3
65
6xy
6.3 – Simplifying Complex Fractions
6xy
LCD:
3759
3759
3 5
7 9
6337
6359
3 9
7 5
9 3
7 5
27
35
27
35
63
Outers over Inners
6.3 – Simplifying Complex Fractions
3759
27
35
)5)(7(
)9)(3(
Outers over Inners
512
56
x
xx
512
56
x
xx
52
5
x
xx
6.3 – Simplifying Complex Fractions
