Question 1

Find the domain of the function $$f(x) = \frac{6x^2$}{x^2$ - 9}.$$

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 2

Write the rational expression $$\frac{2x^2$ - 8}{4x} in $$lowest terms.

Accepted Answer

$$\frac{x - 2}{2}$$

Question 3

Simplify the complex fraction $$\frac{\frac{2}{x}}{\frac{4}{x^2$}}.$$

Accepted Answer

Question 4

Perform the indicated operation and simplify: $$\frac{3}{x} + \frac{2}{x^2$}.$$

Accepted Answer

$$\frac{3x + 2}{x^2$}$$

Question 5

Divide: $$\frac{4a^2$ + 9a + 5}{a^2$ + 3a + 2} \div \frac{a + 5}{a + 2}.$$

Accepted Answer

$$\frac{(4a^2$ + 9a + 5)(a + 2)}{(a^2$ + 3a + 2)(a + 5)}$$

Question 6

Solve for $$x$$: $$\frac{2}{x} = \frac{3}{x + 1}.$$

Accepted Answer

$$x = -2$$

Question 7

A 400-foot object hits the ground at a speed of 160 feet per second. Find the height of a cliff over the gorge if a dropped rock hits the ground at a speed of 128 feet per second. (Use $$v = \sqrt{2gh}$$, $$g = 32 ft/s$^2.)$$

Accepted Answer

$$h = 256 ft$$

Question 8

Suppose $$W is $$inversely proportional to $$H. If$$ $$W = 20$$ when $$H = 12$$, find $$W$$ when $$H = 15.$$

Accepted Answer

$$W = 16$$

Question 9

Simplify: $$\frac{2x^2$ - 8}{4x}.$$

Accepted Answer

$$\frac{x - 2}{2}$$

Question 10

If $$Q is $$jointly proportional to $$R$$ and $$S^2$$, and $$Q = 48$$ when $$R = 3$$ and $$S = 4$$, find $$Q$$ when $$R = 2$$ and $$S = 3.$$

Accepted Answer

$$Q = 13.5$$

Question 11

Solve for $$x$$: $$\frac{x}{x-2} = 3.$$

Accepted Answer

Question 12

The product of one more than a number and twice the reciprocal of the number is $$\frac{15}{2}. $$Find the number.

Accepted Answer

$$2$$

Question 13

If Juan can weed the garden in 2 hours and his husband can weed it in 1 hour 20 minutes, how long will it take them to weed the garden together?

Accepted Answer

$$0.8$$ hours

Question 14

Simplify: $$\frac{3x^2$ - 12}{6x}.$$

Accepted Answer

Question 15

Solve for $$x$$: $$\frac{2x}{x+1} = 4.$$

Accepted Answer

Question 16

When an anvil is dropped into a gorge, the speed with which it strikes the ground is proportional to the square root of the distance it falls. An anvil that falls 400 feet hits the ground at 160 ft/s. What is the speed if it falls 100 feet?

Accepted Answer

$$80 ft/s$$

Question 17

Simplify: $$\frac{2x^2$ - 8}{4x}.$$

Accepted Answer

$$\frac{x - 2}{2}$$

Question 18

Solve for $$x$$: $$\frac{3}{x} + \frac{2}{x^2$} = 1.$$

Accepted Answer

$$x = 1, x = -2$$

Question 19

Use synthetic division to divide $$4x^3$$ - $$2x^2 - 5x + 1$ by x - 2$. What is the remainder?

Accepted Answer

$$-7$$

Question 20

If $$y$$ varies directly as $$x$$ and $$y = 10$$ when $$x = 2$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 25$$

Intermediate Algebra Chapter 6 Study Guide – Rational Functions, Equations, and Applications

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