Question 1

Which of the following values is NOT in the domain of the rational expression $$\frac{x+3}{x^2$-2x-15}$$?

Accepted Answer

$$x = -5$$

Question 2

Simplify the rational expression $$\frac{14x^3$y^2$$}{$$21x^2y^5$}.$$

Accepted Answer

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

Question 3

Which of the following is the correct simplification of $$\frac{2x-1}{1-2x}$$?

Accepted Answer

$$-\frac{2x-1}{1-2x}$$

Question 4

Multiply and simplify: $$\frac{8x^3$}{3y^2$} \cdot \frac{9y^3$}{16x^4$}.$$

Accepted Answer

$$\frac{3y}{2x}$$

Question 5

Divide and simplify: $$\frac{15m^3$}{6n^2$} \div \frac{9m^4$}{12n^4$}.$$

Accepted Answer

$$\frac{10n^2$}{9m}$$

Question 6

What is the least common denominator (LCD) for $$\frac{1}{9} + \frac{3}{n}$$?

Accepted Answer

$$9n$$

Question 7

Add and simplify: $$\frac{5}{x-4} + \frac{x-1}{x-4}.$$

Accepted Answer

$$\frac{x+4}{x-4}$$

Question 8

Subtract and simplify: $$\frac{x+3}{x-6} - \frac{x+4}{x+6}.$$

Accepted Answer

$$\frac{(x+3)(x+6)-(x+4)(x-6)}{(x-6)(x+6)}$$

Question 9

Simplify the complex fraction $$\frac{\frac{9x^2$}{25y^2$z}}{\frac{3x^2$z}{5y^4$}}.$$

Accepted Answer

$$\frac{3y^2$}{5z^2$}$$

Question 10

Solve the rational equation $$\frac{x}{9} - \frac{x}{8} = 1.$$

Accepted Answer

$$x = -72$$

Question 11

A painter can paint a room in 6 hours. His apprentice can paint the same room in 9 hours. How long will it take them to paint the room if they work together?

Accepted Answer

$$3.6$$ hours

Question 12

Tom and Beth can canoe 12 miles down the river in the same time it takes them to canoe 10 miles up the river. The speed of the current is 1 mph. How fast can Tom and Beth paddle the canoe in still water?

Accepted Answer

$$5.5$$ mph

Question 13

Which of the following is an extraneous solution for the equation $$\frac{x^2$-3}{x+2} = \frac{2x+5}{x+2}$$?

Accepted Answer

$$x = -2$$

Question 14

If one number is 6 times another, and the sum of their reciprocals is $$\frac{1}{2}$$, what are the two numbers?

Accepted Answer

$$2$$ and $$12$$

Question 15

John rides a 25-mile trail, part on level ground at 12 mph and part in hills at 8 mph. If he completes the trail in 2.5 hours, how many miles did he ride on level ground?

Accepted Answer

$$15$$ miles

Question 16

Add and simplify: $$\frac{3}{10x^3$y} + \frac{1}{15xy^2$}.$$

Accepted Answer

$$\frac{9y+2x^2$}{30x^3$y^2$$}$

Question 17

Which of the following is the correct LCD for $$\frac{2}{x^3$} - \frac{3}{8x}$$?

Accepted Answer

$$8x^3$$

Question 18

Simplify the complex fraction $$\frac{a^3$}{\frac{1}{a-1} + \frac{1}{b}}$$ using multiplication to clear denominators.

Accepted Answer

$$\frac{a^3$(a-1)b}{b + a-1}$$

Question 19

If Tom and Frank can paint an apartment in 12 hours together, and Tom alone can paint it in 18 hours, how long does it take Frank alone?

Accepted Answer

$$36$$ hours

Intermediate Algebra: Rational Expressions and Equations (Chapter 7 Study Guide)

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