Download Chapter 7: Rational Expressions

Chapter 7: Rational
Expressions
Section 7.4: Adding and Subtracting Rational
Expressions
Section 7.4: Adding and Subtracting
Rational Expressions
Goal: To add and subtract rational expressions
Section 7.4: Adding and Subtracting
Rational Expressions
To find 5/6 – 1/4, you must first find the least common
denominator (LCD). The LCD is the least common
multiple (LCM) of the denominators.
To find the LCM of two or more numbers or polynomials,
factor each number or polynomial. The LCM contains each
factor the greatest number of times it appears as a factor
LCM of 6 and 4
LCM of a2 – 6a + 9 and a2 + a – 12
6=2·3
4 = 22
– 12 = (a – 3)(a + 4)
a2 – 6a + 9 = (a – 3)2
a2 + a
Section 7.4: Adding and Subtracting
Rational Expressions
Example 1
Find the LCM of 15a2bc3, 16b5c2, and 20a3c6
Section 7.4: Adding and Subtracting
Rational Expressions
Add and Subtract Rational Expressions
As with fractions, to add or subtract rational expression, you
must have common denominators
Specific Case
2/3 + 3/5
General case
a/c + b/d
Section 7.4: Adding and Subtracting
Rational Expressions
Example 3
Simplify
2
5a
9
+
2 2
6b 14a b
Section 7.4: Adding and Subtracting
Rational Expressions
Example 4
Simplify
x +10 3x +15
3x -15 6x - 30
Section 7.4: Adding and Subtracting
Rational Expressions
Example 5
Simplify
3x - 5 2 - 7x
- 2
2
x +1 x +1
Section 7.4: Adding and Subtracting
Rational Expressions
Example 6
Simplify
5x
2x
- 2
4y + 8 y + 2y
Section 7.4: Adding and Subtracting
Rational Expressions
Example 7
Simplify
2
2
1
- 2
- 2
x + 3 x + 4x + 3 x + x
Section 7.4: Adding and Subtracting
Rational Expressions
Example 8
Simplify
1 1
+
a b
1
-1
b
Section 7.4: Adding and Subtracting
Rational Expressions
Example 9
Find the slope of the line that passes through P(3/k, 1/3)
and Q(1/2, 2/k)
Section 7.4: Adding and Subtracting
Rational Expressions
Homework:
Practice Exercises: Pg. 325 #2 – 40 (even)