$$\frac{(x+2)(x-2)}{(x-2)(x-3)} = \frac{x+2}{x-3},\ x \neq 2,\ x \neq 3$$

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.

Question 2

Given the rational expression $$\frac{3x+3}{x^2$-1}$$, what is its simplified form?

Accepted Answer

Question 3

What is the domain of the rational expression $$\frac{3x+3}{x^2$-1}$$?

Accepted Answer

$$x 
eq 1,\ x 
eq -1$$

Question 4

Simplify the expression $$\frac{6x+4}{2x-8} \cdot \frac{x-4}{9x+6}.$$

Accepted Answer

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

Question 5

Which value(s) must be excluded from the domain of $$\frac{6x+4}{2x-8} \cdot \frac{x-4}{9x+6}$$?

Accepted Answer

$$x = 4,\ x = -\frac{2}{3}$$

Question 6

Simplify $$\frac{x^2$-9}{x^2$-6x+9} \cdot \frac{5x-15}{x+3}$$ and state any restrictions.

Accepted Answer

$$5$$,\ x 
eq 3,\ x 
eq -3$

Question 7

What is the result of $$\frac{4}{3-x} + \frac{2x}{x-3}$$?

Accepted Answer

$$-2$$

Question 8

Which of the following is a necessary step when simplifying a rational expression?

Accepted Answer

Factor both the numerator and denominator completely.

Question 9

If $$f(x) = \frac{(x+3)(x-1)}{(x+4)(x+4)}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq -4$$

Question 10

Which of the following best describes why $$x = 1 is $$excluded from the domain of $$\frac{3x+3}{x^2$-1}$$?

Accepted Answer

It makes the denominator zero.

Question 11

Given $$\frac{x^2$-16}{x^2$-8x+16}$$, what is the simplified form and domain?

Accepted Answer

$$\frac{x+4}{x-4},\ x 
eq 4$$

Question 12

Which of the following is the correct process for dividing rational expressions?

Accepted Answer

Multiply by the reciprocal of the divisor.

Question 13

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

Accepted Answer

$$ad = bc$$

Question 14

Which of the following is a restriction for the rational expression $$\frac{1}{x(x+h)}$$?

Accepted Answer

$$x 
eq 0,\ x 
eq -h$$

Question 15

What is the simplified form of $$\frac{x^2$-4}{x^2$-5x+6}$$?

Accepted Answer

$$\frac{(x+2)(x-2)}{(x-2)(x-3)} = \frac{x+2}{x-3},\ x 
eq 2,\ x 
eq 3$$

Question 16

Which of the following is the correct way to add $$\frac{1}{x}$$ and $$\frac{1}{x+h}$$?

Accepted Answer

Question 17

If $$x = 3 is a $$restriction for a rational expression, what does this mean?

Accepted Answer

The expression is undefined at $$x = 3.$$

Question 18

Which of the following is the correct simplified form of $$\frac{x^2$-25}{x^2$-10x+25}$$?

Accepted Answer

$$\frac{x+5}{x-5},\ x 
eq 5$$

Rational Expressions and Their Simplification in Precalculus

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