Transcript Rational Equations and Partial Fractions

Rational Equations and Partial Fractions
The purpose of this lesson is solving
Rational Equations (aka:fractions) and
breaking a rational expression into partial
fractions (called Decomposition of
Fractions)
 The use: solving equations with fractions,
developing a sense of logic on how
fractions can be broken down in to parts.

Rational Equations and Partial Fractions
Solving Rational Equations can be solved
by converting to a common denominator
or multiplying both sides of an equation by
the LCD.
 Find the LCD: make a product of the
different factors to the highest power.
 Example: 3(x-1)2(x+2), 5(x-1)(x+2)3(x-5)

Rational Equations and Partial Fractions

Now with a rational
equation
x
2
20

 2
x  4 x  1 x  3x  4
Rational Equations and Partial Fractions

Decompose Fractions
6x  2
a
b


2
x  3x  10 x  5 x  2
Rational Equations and Partial Fractions
( x  2)( x  1)
Solving Rational
Inequalities
2
(
x

3
)(
x

4
)
 Find f(x)=0 values
from numerator and
excluded values from
the denominator
 Lay those points out
on a number line and
test convenient points
for truth or
consequences

0
Rational Equations and Partial Fractions
Find denominator exclusions, then multiply both sides by lcd and solve.
Place values on number line and test regions for truth by using
convenient values.
1
2

1
3b 5b