Here the denominators are 5 and 10, so we
can write
28

6.4: Method 2 for Simplifying Complex Fractions
The second approach interprets the complex fraction as
division and applies the earlier work in dividing fractions in
which you
invert
and
multiply
.
Recall that by the
fundamental principle
we can always
multiply the numerator and denominator of a fraction by the
same nonzero quantity.
29

6.4.1: Use the Fundamental Principle to Simplify Complex
Fractions
Examples:
Simplify the followings:
1.
2.
30

6.4.2: Use division to simplify complex fractions
Examples:
Simplify the following:
1.
2.
31
2
6
5
4
18
3
2
2
2
x
x
x
x
x
x

6.4.2: Use division to simplify complex fractions
The following algorithm summarizes our work with complex fractions.
32

6.5: Solving Rational Equations
Rational Equations
Applications of algebra will often result in equations involving
rational expressions.
The objective in this section is to develop methods to find
solutions for such equations.
The usual technique for solving such equations is to multiply
both sides of the equation by the
least common denominator
(LCD)
of all the rational expressions appearing in the
equation.
The resulting equation will be cleared of fractions, and we can
then proceed to solve the equation as before.
33

6.5: Solving Rational Equations
Examples:
Solve the following rational equations:
1.
2.
3.
34

6.5: Solving Rational Equations
Examples:
Solve the following rational equations:
1.
2.
3.
35

6.5: Solving Rational Equations
Examples:
Solve the following rational equations:
1.
2.
36
1
6
6
1
3
3
3
1
2
x
x
x
x
x
x
1
6
2
7
3
5
x
x
x

6.5: Solving Rational Equations
The following algorithm summarizes our work in solving
equations containing rational expressions.
37

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