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Adding and Subtracting
Rational Expressions
September 16, 2014
SWBAT: Adding and Subtracting rational expressions
SWBAT: Add and Subtract Rational Expressions
Take Warm – Up Worksheet from my desk
You have ~ 20 minutes to
practice!
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
Example 1: Add the fractions and reduce to lowest terms. Step 1: __________________________ Step 2: ___________________________ Step 3: ___________________________
Common Denominator
Combine like terms in numerator
Reduce and simplify.
3b 5b 5x 50
5(x + 10)
SWBAT: Add and Subtract Rational Expressions
= 𝟖𝐛
𝐛𝟐
=𝟖
𝐛
= 𝟖𝐛𝟏−𝟐
=5
2m + 4 2
2m + 6
= 𝟐(𝐦+𝟑)
(𝐦+𝟑)(𝐦 −𝟑)
= 𝟐
𝒎−𝟑
SWBAT: Add and Subtract Rational Expressions
Practice: Add the fractions and reduce to lowest terms.
SWBAT: Add and Subtract Rational Expressions
𝟔𝒙
𝟖 =
𝟑𝒙
𝟒
𝟐𝟖𝒄
𝟏𝟐𝒅=
𝟕𝒄
𝟑𝒅
𝒙+𝟑
𝒙𝟐−𝟗
=𝒙 + 𝟑
𝒙 + 𝟑 (𝒙 − 𝟑)
=𝟏
(𝒙 − 𝟑)
= 𝟐𝒙+𝟔
(𝒙+𝟑)
= 𝟐(𝒙+𝟑)
(𝒙+𝟑)
= 2
SWBAT: Add and Subtract Rational Expressions
Change Subtraction to Addition
Common Denominator
Combine like terms in numerator
Reduce and simplify.
Keep Change Negate
SWBAT: Add and Subtract Rational Expressions
10x 2x
8x
5a + 2 2a -4
5a + 2 – 2a + 4
3a + 6
𝟑(𝐚 + 𝟐)
(𝐚 + 𝟐)(𝐚 − 𝟐)
𝟑
(𝒂 − 𝟐)
3m – 6 -m+2
3m – 6 + m - 2
4m - 8
𝟒
(𝒎 + 𝟑)
𝟒(𝐦 − 𝟐)
(𝐦 + 𝟑)(𝐦 − 𝟐)
SWBAT: Add and Subtract Rational Expressions
= 𝟏𝟏𝒃−𝟒𝒃
𝟑𝒚 =
𝟖𝐱 − 𝟒 − (𝟒𝐱 − 𝟔)
𝟐𝐱 + 𝟔
=𝟖𝐱 − 𝟒 − 𝟒𝐱 + 𝟔
𝟐𝐱 + 𝟔
=𝟒𝒙 + 𝟐
𝟐𝒙 + 𝟔
=𝟐(𝟐𝒙 + 𝟏)
𝟐(𝒙 + 𝟑)
=𝟐𝐱 + 𝟏
𝐱 + 𝟑
= 𝟕𝒃
𝟑𝒚
SWBAT: Add and Subtract Rational Expressions
=𝟔𝒙 − 𝟓 − (𝟓𝒙 − 𝟔)
𝒙𝟐 − 𝟏
=𝟔𝐱 − 𝟓 − 𝟓𝐱 + 𝟔
(𝐱 − 𝟏)(𝐱 + 𝟏)
=(𝐱 + 𝟏)
(𝐱 − 𝟏)(𝐱 + 𝟏)
=𝟏
𝐱 − 𝟏
= 𝟐𝐱+𝟏𝟒−(−𝟐𝐱+𝟐)
𝐱𝟐+𝟐𝐱−𝟑
=𝟐𝐱 + 𝟏𝟒 + 𝟐𝐱 − 𝟐
𝐱𝟐 + 𝟐𝐱 − 𝟑
=𝟒𝒙 + 𝟏𝟐
𝒙𝟐 + 𝟐𝒙 − 𝟑
=𝟒(𝐱 + 𝟑)
(𝐱 + 𝟑)(𝐱 − 𝟏)
=𝟒
𝐱−𝟏
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
SWBAT: Add and Subtract Rational Expressions
= 𝟐𝒂 + 𝟔 + 𝒂𝟐 + 𝟑𝒂 − 𝟐𝟎
𝒂 − 𝟐
= 𝒂𝟐 + 𝟓𝒂 − 𝟏𝟒
𝒂 − 𝟐
-14
5 -2 7
= (𝒂 + 𝟕)(𝒂 − 𝟐)
𝒂 − 𝟐
= a + 7