The
least common denominator
is the simplest polynomial
that is divisible by each of the individual denominators.
Each expression in the desired sum or difference is then “built up”
to an equivalent expression having that LCD as a denominator.
We can then add or subtract as before.
21

6.3.1: Add and Subtract Rational Expressions
Although in many cases the LCD is found by inspection, the
following algorithm is proposed for finding the LCD that is similar
to the one used in arithmetic.
22

6.3.1: Finding the LCD for Two Rational Expressions
Examples:
Find the LCD for each of the following pairs of
rational expressions
1.
2.
3.
4.
23

6.3.1: Add and Subtract Rational Expressions
Examples:
Add or subtract as indicated.
1.
2.
3.
24

6.3.1: Add and Subtract Rational Expressions
Examples:
Add or subtract as indicated.
1.
2.
3.
4.
25
x
x
x
x
2
2
1
2
3
4

6.4: Complex Fractions
Objectives:
6.4.1: Use the fundamental principle to simplify
complex fractions
6.4.2: Use division to simplify complex fractions
26

6.4: Complex Fractions
A
complex fraction
is a fraction that has a fraction in its
numerator or denominator (or both).
Examples of complex fractions:
Two methods can be used to simplify complex fractions.
Method 1 involves the fundamental principle, and method 2
involves inverting and multiplying.
27

6.4: Method 1 for Simplifying Complex Fractions
Recall that by the
fundamental principle
you can always
multiply the numerator and denominator of a fraction by the
same nonzero quantity.
In simplifying a complex fraction, you need to multiply the
numerator and denominator by the LCD of all fractions that
appear within the complex fraction.

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- Fall '18
- jane
- Accounting, Rational Expressions, Fractions, Fraction, Elementary arithmetic, Division of Rational Expressions