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

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