Example
𝑥2
𝑥−1∙𝑥+1𝑥+2
÷𝑥
(𝑥−1)(𝑥+2)ANSWER x(x+1)
Example
𝑥2−42𝑥2−5𝑥+2
÷2 𝑥2−3 𝑥−24 𝑥2−1ANSWER
Example
𝑟2+4𝑟𝑠+3 𝑠2
𝑟2+5𝑟𝑠+6𝑠2∙ (𝑟+2𝑠 )− 1÷ 𝑟+𝑠
𝑟2+4𝑟𝑠+4 𝑠2ANSWER 1
Adding and Subtracting
Rational Expressions
Advanced Math Topics
Mrs. Mongold
Adding and Subtracting Rational
Expressions• Finding Least Common Multiples and Least
Common Denominators!o Use prime factorization
o Example: Find the LCM of 6 and 4• 6 = 2·3• 4 = 22
• LCM= 22·3 = 12
Find the LCM• 1. a2 – 6a + 9 and a2 + a -12
Find the LCM• 2. 18r2s5, 24r3st2, and 15s3t
Find the LCM • 3. 12a2b4, 27ac3, and 18a5b2c
Find the LCM• 4. p3 + 5p2 + 6p and p2 + 6p + 9
Find the LCM• 5. q2 – 4q + 4 and q3 – 3q2 + 2q
Find the LCM• 6. 2k3 – 5k2 – 12l and k3 – 8k2 +16k
Find the LCM• 7. x3-x2 – 2x and x2 – 4x + 4
Add and Subtract Rational
Expressions• Same as fractions…
o To add two fractions we find the LCD, the same things is going to happen with rational expressions
Examples• 8. Simplify xy
y
y
x
1815
72
Examples• 9. Simplify 27
1
9
8
abb
a
Examples• 10. Simplify
y
x
xy 5
3
3
2
Examples• 11. Simplify
22
1
8
1
mnnm
Examples• 12. Simplify
ab
d
b
c
3
2
7
62
Examples• 13. Simplify
82
4
164
12
w
w
w
w
Examples • 14. Simplify
62
6
186
6
x
x
x
x
Examples• 15. Simplify
2012
1
583
12
x
x
xx
x
Homework• 1.
• 2.
• 3.
• 4.