9.5 – adding and subtracting rational expressions
DESCRIPTION
9.5 – Adding and Subtracting Rational Expressions. In order to add or subtract fractions we need a common denominator. LCD: 15. LCD: 36. We want the Lowest Common Denominator (LCD) before we add or subtract. ADDING and SUBTRACTING RATIONALS - Finding LCM. - PowerPoint PPT PresentationTRANSCRIPT
9.5 – Adding and Subtracting Rational Expressions
In order to add or subtract fractions we need a common denominator
53
31
94
12
x
We want the Lowest Common Denominator (LCD) before we add or subtract
LCD: 15 LCD: 36
ADDING and SUBTRACTINGRATIONALS - Finding LCM
• 10x², 35x² _______________________
• 4x³ , 5x²y _______________________
• x-y , x²-y² _______________________
• x²-5x+4 , x – 2 ___________________
70x²
20x³y
(x-y)(x+y)
(x-4)(x-1)(x-2)
ADDING and SUBTRACTINGAdding
• ADD/SUBTRACT Rules
1) Factor denominators2) Find LCM3) Multiply each term to
get denominator = LCM4) +/- and combine like
terms5) Simplify more if
possible
6x32
4xx
2
)2x(32
)2x)(2x(x
)2x()2x(
)2x(32
)2x)(2x(x
33
)2x)(2x(3)2x(2
)2x)(2x(3x3
)2x)(2x(34x5
ADDING and SUBTRACTINGSubtracting
12420
1225
2
xxx
)2x)(6x(20
)6x(25
22
)2x)(6x(20
)6x(25
)2x()2x(
)2x)(6x(240
)6x)(2x(2)2x(5
)6x)(2x(230x5
)6x)(2x(2)6x(5
)2x(25
Factor denominators
Multiply terms to get LCMs on bottom
Simplify
Combine like terms Factor top
Simplify
ADDING and SUBTRACTING A Toughie
yxy
xyx
yxyx
22
22
yxy
xyx
)yx)(yx(yx 22
yxy
yxx
)yx)(yx(yx 22
)yx(yx(
yxy
)yx()yx(
yxx
)yx)(yx(yx 22
)yx)(yx()yx(y
)yx)(yx()yx(x
)yx)(yx(yx 22
)yx)(yx(yyxxyxyx 2222
)yx)(yx(0
0
FACTOR
FACTOR -OUT
CONVERT
SIMPLIFY
COMBINE
SIMPLIFY
Let’s try one
443
322
2
xxxx
Let’s try one
443
322
2
xxxx
Let’s try one
843
1241
2
xx
xx
Let’s try one
843
1241
2
xx
xx
COMPLEX FRACTIONS
What are complex fractions?
Complex fractions are giant expressions where there are fractions within fractions.
The goal is to simplify them down to normal fractions.
EX – simplify
• SIMPLIFYING COMPLEX FRACTIONS STEPS
1) Find LCM of denoms2) Treat each fraction as
an individual problem. Find the LCM and add or subtract.
3) Divide the rational expressions.
4) Simplify
x11
y1
x1
xxx
xx
yxyy
11
11
xxxyxy
1
1
xx
xyxy
)1(
xyxy
EX - simplify
x112
21x
1
1x12
21x
1
11
12
11
11
12
11
xxx
xx
x
1122
1221
xxxx
321
112
xx
xx
3x2
3x2
FACTOR OUT -1
MULT TOP/BOT by LCM
DISTRIBUTE LCM
SIMPLIFY
SIMPLIFY
132112
xxxx
DIVIDE THE RATIONALS
Let’s try one
11
13
122
xxxxx
Let’s try one
11
13
122
xxxxx