Question 1

Which of the following is the correct definition of a rational expression?

Accepted Answer

An expression that can be written as the ratio of two polynomials, where the denominator is not zero.

Question 2

Simplify the following rational expression: $\frac{6x^2}{9x}$

Accepted Answer

$\frac{2x}{3}$

Question 3

Which value of $x$ makes the rational expression $\frac{2x+5}{x-3}$ undefined?

Accepted Answer

$x = 3$

Question 4

A chemist is mixing two solutions. The concentration of the first solution is represented by $\frac{4x}{x+2}$ and the second by $\frac{3x}{x-2}$. What is the sum of the concentrations?

Accepted Answer

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

Question 5

Simplify the following expression: $\frac{x^2-9}{x^2-6x+9}$

Accepted Answer

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

Question 6

A medical researcher is analyzing the rate of a drug's absorption, modeled by $\frac{5t}{t^2+4}$. What is the value of the expression when $t=2$?

Accepted Answer

$\frac{10}{8}$

Question 7

Which of the following is equivalent to $\frac{2}{x} + \frac{3}{x}$?

Accepted Answer

$\frac{5}{x}$

Question 8

If $\frac{a}{b} = \frac{c}{d}$ and $b, d 
eq 0$, which of the following is true?

Accepted Answer

$ad = bc$

Question 9

A company’s profit per item is modeled by $P(x) = \frac{10x-20}{x}$, where $x$ is the number of items sold. What is the profit per item if 5 items are sold?

Accepted Answer

$2$

Question 10

Simplify the following complex fraction: $\frac{\frac{3}{x}}{\frac{6}{x^2}}$

Accepted Answer

$\frac{x}{2}$

Question 11

Which of the following is NOT a valid step when simplifying $\frac{x^2-4}{x^2+2x}$?

Accepted Answer

Cancelling $x-2$ from numerator and denominator

Question 12

A biologist models the population growth rate of a species as $\frac{2n+4}{n^2-4}$. For which value of $n$ is the expression undefined?

Accepted Answer

$n = 2$ and $n = -2$

Question 13

Simplify the following expression: $\frac{x^2-16}{x^2+8x+16}$

Accepted Answer

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

Question 14

A rational expression is undefined for which of the following values of $x$ in $\frac{5x}{x^2-9}$?

Accepted Answer

$x = 3$ and $x = -3$

Question 15

If $\frac{a}{b} + \frac{c}{d} = \frac{ad+bc}{bd}$, which of the following is the sum of $\frac{2}{3} + \frac{5}{4}$?

Accepted Answer

$\frac{23}{12}$

Question 16

A rational function models the speed of a chemical reaction: $R(t) = \frac{8t}{t^2+1}$. What is the value of $R(1)$?

Accepted Answer

$\frac{8}{2}$

Question 17

Which of the following is the correct way to multiply $\frac{2x}{3}$ and $\frac{9}{4x}$?

Accepted Answer

$\frac{2x \cdot 9}{3 \cdot 4x}$

Question 18

A rational expression is simplified to $\frac{1}{x-2}$. For which value of $x$ is this expression undefined?

Accepted Answer

$x = 2$

Question 19

If $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$, what is $\frac{3}{4} \div \frac{2}{5}$?

Accepted Answer

$\frac{15}{8}$

Rational Expressions: Homework Overview and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards