A29­5Notes.notebook
November 13, 2015
Algebra 2
Ch.9 Notes Page 53
P53 9­5 Add/Subtract Rational Expressions
Aug 19­6:20 AM
Least Common Multiples
Find the Least Common Multiple of 4x2 ­ 36 and 6x2 + 36x + 54
Factor First
4x2 ­ 36 = 4(x2 ­ 9) = 2 x 2 (x + 3)(x ­ 3)
6x2 + 36x + 54 = 6(x2 + 6x + 9) = 2 x 3 (x + 3)(x + 3)
Write each prime factor the greatest number of times
it appears in either expression. Simplify!
2 x 2 x 3 (x ­ 3)(x + 3)(x + 3)
12(x ­ 3)(x + 3)2
Feb 16­2:55 PM
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A29­5Notes.notebook
November 13, 2015
Find the Least Common Multiple of 3x2 ­ 9x ­ 30 and 6x + 30
Dec 7­2:01 PM
Adding Rational Expressions
You Must have a Common Denominator to Add Fractions!
Factor the Denominators
Multiply each Fraction by what is in the Other Denom.
Simplify and Add
(You have a Common Denom.)
Final Answer
1 + 5x x2 + 5x + 4 3x + 3 1 + 5x (x + 1)(x + 4) 3(x + 1) 3 1 + (x+4) 5x 3 (x + 1)(x + 4) (x+4) 3(x + 1) 3 + 5x(x+4) 3(x + 1)(x + 4) 3(x + 1)(x+4) 5x2 + 20x + 3
3(x + 1)(x + 4)
Feb 16­2:55 PM
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A29­5Notes.notebook
November 13, 2015
Adding Rational Expressions
1 + 3x x2 ­ 4x ­ 12 4x + 8 Dec 7­2:01 PM
Subtracting Rational Expressions
You Must have a Common Denominator to Subtract Fractions!
Factor the Denominators
7y ­ 4 5y2 ­ 125 3y + 15 7y ­ 4 5(y+5)(y­5) 3(y+5) Multiply each Fraction by what is in the Other Fraction
3 7y ­ 5(y­5) 4 3 5(y+5)(y­5) 5(y­5) 3(y+5) Simplify and Add
(You have a Common Denom.)
21y ­ 20y ­ 100 15(y+5)(y­5) 15(y+5)(y­5) Final Answer
1y + 100 15(y+5)(y­5) Feb 16­2:56 PM
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A29­5Notes.notebook
November 13, 2015
Subtracting Rational Expressions
x ­ 2x + 1 3x2 ­ 9x + 6 3x2 + 3x ­ 6 Dec 7­2:03 PM
HW #56
9­5 WS
Please put your name and class period at the top of
the homework. Also include the homework number.
Aug 19­6:25 AM
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