A.3b Rational Expressions
We ourselves feel that what we are doing is just a drop in
the ocean. But the ocean would be less because of that
missing drop. -Mother Teresa
More Factoring Practice
Factor completely.
3(4x  5)2  4(5x 1)2  (4 x  5)3  2(5x 1)  5


Simplifying Rational Expressions
Now that we know how to factor, we can use it to
simplify rational expressions!
Rational Expression: the quotient of two polynomials
Ex.
x 4
x2  x  6
2
numerator
denominator
Products of Rational Expressions
Recall: When we multiply fractions, we multiply numerators
and multiply denominators
x 2  2x  1 4 x 2  4
 2
3
x x
x  x 2
Products of Rational Expressions
Now you try!

x 2  7x  8 x 3  x 2
 2
4
3
4 x  32x
x 1
Adding/Subtraction Rational Expressions
Add the following rational expressions. Leave your answer in
factored form.
1
x
x2


x4

Adding/Subtraction Rational Expressions
Add the following rational expressions. Leave your answer in
factored form.
x
2x  3
 2
2
x  3x  2 x 1
x 2  3x  2 
x 2 1 


Adding/Subtraction Rational Expressions
Add the following rational expressions. Leave your answer in
factored form.
x
2x  3

(x  2)(x  1) (x  1)( x 1)
LCM : (x  2)( x  1)(x 1)
Adding/Subtraction Rational Expressions
Want one to try? Okay!

2x 1
x
 2
2
x  x  6 x  3x
A.3b Rational Expressions
Homework:
Page 976
#57 - 77 EOO
We ourselves feel that what we are doing is just a drop in
the ocean. But the ocean would be less because of that
missing drop. -Mother Teresa