Adding and Subtracting Three Rational ExpressionsAdd and subtract as indicated.
Factor the third denominator.Add and subtract the numerators.Distributive propertyCombine like terms in the numerator.Factor the numerator.Lowest terms
NOW TRYSubtracting Rational ExpressionsSubtract.
If we try to factor the numerator, we find that this rational expression is in lowest
terms.
=
- m^2 + 3 m- 5
1 m- 321 m+ 121 m- 22
=
m^2 + 2 m- 8 - 2 m^2 + m+ 3
1 m- 321 m+ 121 m- 22
=
m^2 + 2 m- 8 - 12 m^2 - m- 32
1 m- 321 m+ 121 m- 22
=
1 m+ 421 m- 22 - 12 m- 321 m+ 12
1 m- 321 m+ 121 m- 22
=
1 m+ 421 m- 22
1 m- 321 m+ 121 m- 22
-
12 m- 321 m+ 12
1 m- 321 m- 221 m+ 12
=
m+ 4
1 m- 321 m+ 12
-
2 m- 3
1 m- 321 m- 22
m+ 4
m^2 - 2 m- 3
-
2 m- 3
m^2 - 5 m+ 6
EXAMPLE 7
=
8
x
=
81 x- 22
x 1 x- 22
=
8 x- 16
x 1 x- 22
=
3 x+ 5 x- 10 - 6
x 1 x- 22
=
3 x+ 51 x- 22 - 6
x 1 x- 22
=
3 x
x 1 x- 22
+
51 x- 22
x 1 x- 22
-
6
x 1 x- 22
=
3
x- 2
+
5
x
-
6
x(x-2)
3
x- 2
+
5
x
-
6
x^2 - 2 x
EXAMPLE 6
376 CHAPTER 7 Rational Expressions and Functions
NOW TRYThe LCD is
fundamental propertyx 1 x- 22 ;Factor each
denominator.The LCD is
1 m+ 121 m- 22.1 m- 32 #
Subtract the
numerators.Multiply in the
numerator.Distributive
propertyCombine like terms
in the numerator.Be careful
with signs.Note the
careful use of
parentheses.NOW TRY
EXERCISE 6
Add and subtract as indicated.
6
y-
1
y- 3+
3
y^2 - 3 yNOW TRY ANSWERS
- t^2 + 5 t+ 11
1 t+ 221 t- 421 t+ 12
5
yNOW TRY
EXERCISE 7
Subtract.
t- 1
t^2 - 2 t- 8-
2 t+ 3
t^2 + 3 t+ 2