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Chapter 6 Rational
Equations
Rational expressions
• These have a variable in the denominator Ex:
1/x
• We have to be careful of "non-permissible"
values. These are numbers that give an
undefined value.
Ex: state the non-
permissible value(s)
Ex: state the non-
permissible values (NPVs)
What should replace ?
State the operation to change
the 1st to the 2nd expression
Divide top and bottom by pq?
Simplify and state any NPVs
Simplify and state any NPVs
P. 317 q's 1-9, 18
Operations with rational
expressions
• Remember to watch for NPVs!
• Factor any polynomials first, then simplify
• When dividing, multiply by the reciprocal
Operations with rational
expressions
Ex:
simplify m
c
cf
fm
4
15
5
12 2
m
c
cf
fm
1
3
1
3 2
• First: cancel out common factors
• Next: cancel out or combine common variables
and write as a single fraction or term
0,,;9 mfcm
Ex: simplify & ID any NPVs
Ex: simplify & ID any NPVs
6.3 More operations
• Careful to make sure the denominators are
equal to add or subtract fractions!
• Continue to pay attention to NPVs
Ex: simplify
Ex: simplify
Ex: simplify
P. 336 q's 1-9, 20
Mini-quiz tomorrow (Venus day)
Quiz #4
48
358
3
58
22
4
xy
yx
xy
yx
358
48
3
58 2
2
4
yx
xy
xy
yx
1524
3244
333
58 2
2
4
yx
yx
yx
yx
Quiz #4
15
198
x
y
Quiz #5
)73)(73(
)73)(158(
xx
xx
6.4 Rational Equations • Can we use our rational skills to solve the
problem?
Ex: solve for f
1213 f 1f
Ex: solve
Ex: word problem
• Two hoses together fill a pool in 2h, but hose A
fills the pool in 3h. How long to fill the pool using
only hose B?
• Try writing a rational equation representing what
fractions of the pool are filled in one hour
P. 348 q's 1-7, 22
Chapter Review P. 352
odds
Practice Test P. 355
odds
