Step 3
Distributive property
Multiply.
Distributive property
Combine like terms.
Subtract 15.
Proposed solution Divide by
Step 4 Since the proposed solution, 3, is not in the domain, it cannot be a solution
of the equation. Substituting 3 into the original equation shows why.
CHECK Original equation
Let
Division by 0 is undefined.
The equation has no solution. The solution set is 0. NOW TRY
2
0
-
3
6
^12
0
x=3.
2
3 - 3
-
3
3 + 3
^12
32 - 9
2
x- 3
-
3
x+ 3
=
12
x^2 - 9
x= 3 - 1.
- x=- 3
- x+ 15 = 12
2 x+ 6 - 3 x+ 9 = 12
21 x+ 32 - 31 x- 32 = 12
= 1 x+ 321 x- 32 c
12
1 x+ 321 x- 32
d
1 x+ 321 x- 32 a
2
x- 3
b - 1 x+ 321 x- 32 a
3
x+ 3
b
388 CHAPTER 7 Rational Expressions and Functions
NOW TRY
EXERCISE 3
Solve.
1
t- 7
+
2
t+ 7
=
14
t^2 - 49
NOW TRY
EXERCISE 4
Solve.
2
t^2 - 16
2
t^2 - 2 t- 8
-
4
t^2 + 6 t+ 8
=
Solving a Rational Equation
Solve
Factor each denominator to find the domain and the LCD.
Factor the denominators.
The domain excludes 1, , and. Multiply each side of the equation by the LCD,
Distributive property
Distributive property
Combine like terms.
Subtract 4p. Add 7.
Proposed solution Divide by 3.
Note that 3 is in the domain. Substitute 3 for pin the original equation to check that
the solution set is 536. NOW TRY
3 =p
9 = 3 p
4 p+ 2 = 7 p- 7
6 p+ 6 - 2 p- 4 = 7 p- 7 2 # 3 =6;
2 # 31 p+ 12 - 21 p+ 22 = 71 p- 12
= 21 p- 121 p+ 221 p+ 12 c
7
21 p+ 221 p+ 12
d
21 p- 121 p+ 221 p+ 12 c
3
1 p- 121 p+ 22
-
1
1 p+ 121 p- 12
d
21 p- 121 p+ 221 p+ 12.
- 2 - 1
=
7
21 p+ 221 p+ 12
3
1 p- 121 p+ 22
-
1
1 p+ 121 p- 12
3
p^2 + p- 2
-
1
p^2 - 1
=
7
21 p^2 + 3 p+ 22
.
EXAMPLE 4
NOW TRY ANSWERS
- 0 4. 556