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

Study Guide - Practice Questions

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