$$\dfrac{3}{x-1},\ x \neq 1, -1$$

Question 1

Which of the following is a rational expression?

Accepted Answer

$$\dfrac{x^2$ - 3x + 4}{x + 1}$$

Question 2

What is the domain of the rational expression $$\dfrac{(x+4)(x-2)}{(x+5)(x-4)}$$?

Accepted Answer

$$x 
eq -5, 4$$

Question 3

Simplify $$\dfrac{3x+3}{x^2$-1}$$ and state the domain.

Accepted Answer

$$\dfrac{3}{x-1},\ x 
eq 1, -1$$

Question 4

Which value makes the rational expression $$\dfrac{x^2$+2x-8}{x+4}$$ undefined?

Accepted Answer

$$x = -4$$

Question 5

Divide and simplify: $$\dfrac{x^2$+2x-3}{x^2$+8x+16} \div \dfrac{x-1}{3x+12}.$$

Accepted Answer

$$\dfrac{(x+3)(3x+12)}{(x+4)^2$(x-1)}$$

Question 6

Which of the following is the correct first step to simplify $$\dfrac{3x+3}{x^2$-1}$$?

Accepted Answer

Factor numerator and denominator

Question 7

After simplifying $$\dfrac{3x+3}{x^2$-1}$$, what values must be excluded from the domain?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 8

Which of the following best describes a rational expression?

Accepted Answer

A quotient of two polynomials

Question 9

Given $$\dfrac{x^2$+2x-8}{x+4}$$, what is the simplified form?

Accepted Answer

$$x-2$$

Question 10

If $$x = 4$$, what happens to the expression $$\dfrac{(x+4)(x-2)}{(x+5)(x-4)}$$?

Accepted Answer

The expression is undefined

Question 11

Which of the following is NOT a step in simplifying a rational expression?

Accepted Answer

Multiplying numerator and denominator by the same value

Question 12

Why must you specify the domain when simplifying rational expressions?

Accepted Answer

To avoid division by zero

Question 13

Which of the following is equivalent to dividing by a rational expression?

Accepted Answer

Multiplying by its reciprocal

Question 14

Given $$\dfrac{(x+3)(x-1)}{(x+4)(x+4)} 	imes \dfrac{3x+12}{x-1}$$, what is the simplified form?

Accepted Answer

$$\dfrac{3(x+3)}{x+4}$$

Question 15

Which of the following is a common mistake when simplifying rational expressions?

Accepted Answer

Cancelling terms instead of factors

Rational Expressions: Simplification and Division (Precalculus MATH-107 P.5)

Study Guide - Practice Questions