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CH. 9.5 Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions. ALGEBRA 2 LESSON 9-5. Find the least common multiple of 2 x 2 – 8 x + 8 and 15 x 2 – 60. Step 1: Find the prime factors of each expression. - PowerPoint PPT Presentation
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CH. 9.5 Adding and Subtracting Rational Expressions CH. 9.5 Adding and Subtracting Rational Expressions
Find the least common multiple of 2x2 – 8x + 8 and 15x2 – 60.
ALGEBRA 2 LESSON 9-5ALGEBRA 2 LESSON 9-5
Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions
Step 1: Find the prime factors of each expression.
2x2 – 8x + 8 = (2)(x2 – 4x + 4) = (2)(x – 2)(x – 2)
15x2 – 60 = (15)(x2 – 4) = (3)(5)(x – 2)(x + 2)
Step 2: Write each prime factor the greatest number of times it appears in either expression. Simplify where possible.
(2)(3)(5)(x – 2)(x – 2)(x + 2) = 30(x – 2)2(x + 2)
The least common multiple is 30(x + 2)(x – 2)2.
9-5
Check understanding 2A p. 505Check understanding 2A p. 505
Simplify + .
ALGEBRA 2 LESSON 9-5ALGEBRA 2 LESSON 9-5
Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions
13x2 + 21x +30
4x 3x + 15
+ = + Factor the denominators.
13x2 + 21x +30
4x 3x + 15
13(x + 2)(x + 5)
4x 3(x + 5)
= + • Identity for Multiplication.
13(x + 2)(x + 5)
4x 3(x + 5)
x + 2x + 2
= + Multiply.13(x + 2)(x + 5)
4x(x + 2)3(x + 2)(x + 5)
= Add.1 + 4x(x + 2)3(x + 2)(x + 5)
= Simplify thenumerator.
4x2 + 8x +13(x + 2)(x + 5)
= Simplify thedenominator.
4x2 + 8x +13x2 + 21x +30
9-5
Check Understanding 3 p. 506Check Understanding 3 p. 506
ALGEBRA 2 LESSON 9-5ALGEBRA 2 LESSON 9-5
Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions
Simplify - .2x
x2 – 2x – 3 3 4x + 4
– = – Factor the denominators.
2xx2 – 2x – 3
3 4x + 4
2x(x – 3)(x + 1)
3 4(x + 1)
= Simplify.4(2x) – [(3)(x – 3)]
4(x + 1)(x – 3)
= Simplify.5x + 94x2 – 8x – 12
9-5
= • – • Identity for Multiplication.
x – 3x – 3
2x(x – 3)(x + 1)
3 4(x + 1)
44
Check understanding 4b p. 506Check understanding 4b p. 506
Simplify .
ALGEBRA 2 LESSON 9-5ALGEBRA 2 LESSON 9-5
Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions
1x
1y
2y
1x
+
–
1x
1y
2y
1x
+
–
1x
1y
2y
1x
+
–
• xy
• xy= The LCD is xy. Multiply the numerator
and denominator by xy.
2 • xyy
1 • xyx
1 • xyx
1 • xyy+
–
= Use the Distributive Property.
y + x2x – y= Simplify.
Method 1: First find the LCD of all the rational expressions.
9-5
(continued)
ALGEBRA 2 LESSON 9-5ALGEBRA 2 LESSON 9-5
Adding and Subtracting Rational ExpressionsAdding and Subtracting Rational Expressions
= Write equivalent expressions withcommon denominators.
1x
1y
2y
1x
+
–
+
–
yxy
xxy
2xxy
xxy
2x – yxy
x + yxy
= Add.
Method 2: First simplify the numerator and denominator.
= ÷ Divide the numerator fraction by the denominator fraction.
x + yxy
2x – yxy
= • Multiply by the reciprocal.x + y
xyxy
2x – y
=x + y2x – y
9-5
Check understanding 5 a – c p. 507Check understanding 5 a – c p. 507
HomeworkHomework
Page 507 # 4, 6, 9, 10 - 26
CH. 9.3-9.4 Quiz next class
