Equations involving Rational Expressions
To solve:
1. Determine the LCD of the rational expressions.
2. Multiply both sides of the equation by this LCD.
3. Perform the resulting operation and simplify the remaining
terms.
4. Solve the equation that arises.
5. Check the obtained solutions against the original equation
and drop or omit those that will make the rational
expressions undefined.
Remark: The solutions omitted in Step [5] above are
referred to as extraneous roots or extraneous solutions.
These omitted values are not included in the solution set.
For Exercises 5–10,
a. Simplify the expression.
b. Substitute 0 for h in the simplified expression.
2(x + h)? + 3(x + h) ·
5.
(2x + 3x)
3(x + h - 4(x + h) – (3x - 4x)
6.
h
1
1
1
1
(x + h) – 2
7.
x - 2
2(x + h) + 5
8.
2x + 5
h
(x + h) – x
9.
(x + h)
10.
- X
h
h
Exercises 38–40 will help you prepare for the material covered in
the first section of the next chapter.
In Exercises 38-39, simplify each algebraic expression.
38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6)
39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9)
40. The figures show the graphs of two functions.
y
y
201
10-
....
-20-
flx) = x³
glx) = -0.3x + 4x + 2
Chapter A.2 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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