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Simplify Rational Expressions

1. Simplify the rational expression
(6x - 8)/(8 - 6x)

2. Evaluate the expression f(x) = (3x + 2)/ (x) for x = 4

3. The average (mean) cost for a service club to publish a directory of its members is given by the rational function. f(x) = (1.5x + 700)/x

where x is the number of directories printed. Find the average cost per directory for x = 1000.

4. Do the operations and simplify:

(a + 4)/(81 - a^2) . (7a - 63)/(7a + 28)

5. Simplify the radical. (108xy^11)/(3xy). Assume that all variables represent positive numbers.

6. Simplify and combine like radicals: 4^3√216x + 4^3√8x. Assume that x represents a positive number.

7. Do the multiplication and simplify if possible: 3√5(4√5) . Choose the correct answer from the following: 12, 300, or 60..

8. Multiply and simplify the result: 7√2(8√6 + 4√3)

9. Simplify the expression by rationalizing the denominator : √10/5

10. Use factoring to solve each equation.

2z^2= -2 + 5 z

11. Give an example using either completing the square or the quadratic formula and explain each step as if you were teaching someone who had never used the method before.

Solution Preview

1. Simplify the rational expression
(6x - 8)/(8 - 6x)

=-1*(8-6X)/(8 - 6x)

Ans = -1

2. Evaluate the expression f(x) = (3x + 2)/ (x) for x = 4

f(4) =(3*4+2)/4

=14/4 or 3.5

3. The average (mean) cost for a service club to publish a directory of its members is given by the rational function. f(x) = (1.5x + 700)/x

where x is the number of directories printed. Find the average cost per directory for x = 1000.

mean ...

$2.19