# 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 ...

#### Solution Summary

The following posting helps with problems that involve simplifying rational expressions.