12-6 Rational Expressions with Like Denominators

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12-6 Rational Expressions with Like Denominators
12-6
Rational Expressions with Like
Denominators
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restricted.
Objectives
• Students will add rational expressions with
like denominators.
• Students will subtract rational expressions
with like denominators.
Rational
Expressions
• Use common denominators!
Do not reduce before adding!
Example 1
4b 16b 20b 4b
+
=
=
15 15
15
3
Example 2
6c
12
6c + 12 6(c + 2)
+
=
=
=6
c+2 c+2
c+2
c+2
Example 3
7x + 9 x − 5
−
x −3 x −3
7 x + 9 − ( x − 5)
=
x −3
7x + 9 − x + 5
=
x −3
6 x + 14
=
x −3
2(3 x + 7)
=
x −3
Example 4
3x + 2 y
2x + y
5x + 4 y
2x + y
Find an expression
for the perimeter of
the rectangle
pictured.
3x + 2 y 3x + 2 y 5x + 4 y 5x + 4 y
P=
+
+
+
2x + y 2x + y 2x + y 2x + y
16x + 12 y
=
2x + y
4(4 x + 3 y)
=
2x + y
Example 5
3s
− 5s
+
11 − s s − 11
− 3s
− 5s
=
+
s − 11 s − 11
− 8s
=
s − 11
Example 6
2y
7y
−
y−2 2− y
2y
−7y
=
−
y−2 y−2
9y
=
y−2
Image Sources
Death Star [Online Image] Available
http://aspasia.mm.di.uoa.gr/~rouvas/backgrounds/Star-Wars-Wallpaper.jpg 4
May, 2006
Yoda
[Online Image] Available
http://baixaki.ig.com.br/imagens/wpapers/star-wars-episode-3-6800.jpg
Darth Vader [Online Image] Available
http://darthvader.mysteria.cz/Vader/img/logo-vader.jpg4 May, 2006
Darth Vader
[Online Image] Available
http://movie-poster.ws/movies/wallpaper/scifi/starwars/darth_vader.jpg
4 May, 2006
The Star Wars Trilogy – Return of the Jedi [Online Image] Available
http://www.art.com/asp/sp.asp?PD=10135055&RFID=055687
4 May, 2006
300px-An_ewok [Online Image] Available
http://upload.wikimedia.org/wikipedia/en/thumb/2/2b/An_ewok.jpg/300pxAn_ewok.jpg
4 May, 2006
Image Sources
20020418%20BMA-Star%20Wars%20039 [Online Image] Available
http://www.sfrevu.com/ISSUES/2002/0205/Event%20-%20BMAStar%20Wars/20020418%20BMA-Star%20Wars%20039.jpg
4 May, 2006
Chewbacca/Hans Solo [Online Image] Available
http://www.ragjr.com/chewieso.jpg
R2d2 [Online Image] Available
www.galaxy.com/r2d2 4 May, 2006

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