Question 1

Which of the following is the correct domain of the rational function $$f(x) = \frac{7x}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2,\ x 
eq -2$$

Question 2

Simplify the rational expression $$\frac{x^2$ - 9}{x^2$ - 6x + 9} to $$lowest terms.

Accepted Answer

$$\frac{x + 3}{x - 3}$$

Question 3

Which of the following is an equivalent rational expression to $$\frac{a - b}{b}$$?

Accepted Answer

$$-\frac{b - a}{b}$$

Question 4

Given the rational function $$R(t) = \frac{1000}{t^2$ + 4}$$, what is the domain of $$R$$?

Accepted Answer

All real numbers

Question 5

Multiply the rational expressions $$\frac{5x - 20}{3x^2$ + x}$$ and $$\frac{3x^2$ + 12x + 4}{x^2$ - 16}$$ and simplify.

Accepted Answer

$$\frac{5(x - 4)(3x^2$ + 12x + 4)}{(3x^2$ + x)(x - 4)(x + 4)}$$

Question 6

Divide the rational expressions $$\frac{x + 2}{7 - x} by$$ $$\frac{x^2$ - 5x + 6}{x^2$ - 9x + 14}$$ and simplify.

Accepted Answer

$$\frac{x + 2}{7 - x} \cdot \frac{x^2$ - 9x + 14}{x^2$ - 5x + 6}$$

Question 7

Add the rational expressions $$\frac{2}{3}$$ and $$\frac{5}{6}$$ and simplify.

Accepted Answer

$$\frac{3}{2}$$

Question 8

Find the least common denominator (LCD) for the rational expressions $$\frac{5m}{3m^2$ + 15}$$ and $$\frac{2}{m + 5}.$$

Accepted Answer

$$3m(m + 5)$$

Question 9

Write $$\frac{6}{3a} as an $$equivalent expression with denominator $$12ab.$$

Accepted Answer

$$\frac{24b}{12ab}$$

Question 10

Add the rational expressions $$\frac{5x}{x}$$ and $$\frac{7x}{x}$$ and simplify.

Accepted Answer

$$\frac{12x}{x}$$

Question 11

Solve the equation $$\frac{2}{x} = 3$$ for $$x.$$

Accepted Answer

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

Question 12

If $$\frac{a}{b} = \frac{c}{d}$$, what is the cross product property?

Accepted Answer

$$a \cdot d = b \cdot c$$

Question 13

A car travels 280 miles in the same time that a motorcycle travels 240 miles. If the car's speed is 10 mph more than the motorcycle's, what is the speed of the motorcycle?

Accepted Answer

$$56$$ mph

Question 14

Simplify the expression $$\frac{x^2$ + 7}{7 + x}.$$

Accepted Answer

$$\frac{x^2$ + 7}{x + 7}$$

Question 15

Subtract $$\frac{x - 2}{x^2$ - 30}$$ from $$\frac{2x + 3}{x^2$ - 30}$$ and simplify.

Accepted Answer

$$\frac{2x + 3 - (x - 2)}{x^2$ - 30}$$

Question 16

If $$T = \frac{2x}{B + E}$$, solve for $$x.$$

Accepted Answer

$$x = \frac{T(B + E)}{2}$$

Question 17

Convert 3 cubic yards to cubic feet.

Accepted Answer

$$81$$ cubic feet

Question 18

Add the rational expressions $$\frac{3}{4}$$ and $$\frac{5}{6}$$ and simplify.

Accepted Answer

$$\frac{13}{12}$$

Question 19

Given two similar triangles, $$	riangle HJG$$ and $$	riangle KLM$$, with $$HJ = 12$$, $$JG = 18$$, $$KL = 20$$, and $$LM = x$$, what is the value of $$x$$?

Accepted Answer

$$24$$

Rational Expressions and Problem Solving in College Algebra

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