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Find the domain of each rational expression.

Find the domain of each rational expression.
28. x^2 - 3 over x + 9

Reduce each expression to lowest terms.
73. 3a - 2b over 2b - 3a

Perform the indicated operation.
26. b^3 + b over 5 * 10 over b^2 + b
52. (6y2 - y - 2) / 2y + 1 over 3y - 2

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expressionwith the LCD as the denominator.
60. 3 over 8a^3b^9 , 5 over 6a^2c
62. 5 over 12a^6b, 3b over 14a^3, 1 over 2ab^3

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.
68. 5x over x^2 - 1, -4 over x^2 - 2x + 1

Perform the indicated operation. Reduce each answer to lowest terms.
64. 5 over 2x - 4 - 3 over 2 - x

Perform the indicated operation. Reduce each answer to lowest terms.
74. 3 over 4c + 2 - c - 4 over 2c^2 + c - 5 over 6c
24. 1/x + 1/y over 3/x + 3/y
40. 2/x-5 - x over 3x/5-x - 1

Solve each equation. Watch for extraneous solutions.
38. 4/x + 3/x-3 = x/x-3 - 1/3
50. -3/x = x/-3

Find a ratio for each of the following, and write it as a ratio of integers in lowest terms.
26. Hits and misses. A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses?

Solve each proportion.
34. 9/x = 3/2

Solve each formula for the indicated variable.
16. F = mv^2/r for r
18. 1/r = 1/r1 +1/r2 for r

Show a complete solution to each problem.
38. Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling?

Solution Preview

Herewith I have attached the solutions.

1) Find the domain of each rational expression.
28. x^2 - 3 over x + 9
Solution
X + 9 = 0
X = -9
x = -9 is restricted domain.
Therefore, except -9 all the real numbers are the domain of the above rational function.

2) Reduce each expression to lowest terms.
73. 3a - 2b over 2b - 3a
Solution
(3a - 2b)/(2b -3a)

= (3a - 2b)/-(3a - 2b)

= 1/-1

= -1

Perform the indicated operation.
26. b^3 + b over 5 * 10 over b^2 + b
Solution
b^3 +b/5 x 10/b^2 + b
b^3 +10b/5b^2 + b
b^3+ 2/b + b

52. (6y2 - y - 2) / 2y + 1 over 3y - 2
Solution
(6y^2 - y -2)
-----------------
(2y +1)/(3y -2)

Factorizing the numerator, we get
= (3y -2)(2y +1)
--------------------
(2y +1)/(3y -2)
The above expression can be written as.
= (3y -2)(2y +1) (3y -2)
---------------- x ----------
1 (2y +1)
Now we can cancel out the common factor (2x -1), which is both in the numerator and the denominator.

= (3y-2)(3y -2)
= (3y -2)^2

Find the LCD for the given rational expressions, and convert
each rational expression into an equivalent rational expression
with the LCD as the denominator.
60. 3 over 8a^3b^9 , 5 over 6a^2c
Solution
LCD of the above two rational expression is 24a^3b^9c

3/8a^3b^9 = 9 / 24a^3b^9c

5/6a^2c = 20ab^9 / 24a^3b^9c

62. 5 over 12a^6b, 3b over 14a^3, 1 over 2ab^3
Solution
5 / 12a^6b, 3b/14a^3, 1/2ab^3
LCD of the above three rational expression is 84a^6 b^3
5 / 12a^6b ...

Solution Summary

This solution is comprised of a detailed explanation to find the domain of each rational expression.

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