Question 1

Which of the following best describes a rational equation?

Accepted Answer

An equation with a variable in the denominator of a fraction.

Question 2

What is the first step when solving a rational equation according to the provided method?

Accepted Answer

Determine restrictions by setting denominators equal to zero.

Question 3

Given the equation $$\frac{2x}{x-1} = 12$$, which value of $$x$$ must be excluded from the solution set?

Accepted Answer

$$x = 1$$

Question 4

Solve the rational equation $$\frac{x+1}{2} = 5. $$What is the solution?

Accepted Answer

$$x = 9$$

Question 5

Which of the following is a restriction for the equation $$\frac{2}{x} + 4 = 3$$?

Accepted Answer

$$x = 0$$

Question 6

If you solve $$\frac{x}{3} = \frac{2}{x}$$, which step should you take after finding the solution?

Accepted Answer

Check if the solution makes any denominator zero.

Question 7

Solve the equation $$\frac{2x-5}{x-2} = 3. $$What is the solution?

Accepted Answer

$$x = 4$$

Question 8

Why must you check your solution against the restrictions after solving a rational equation?

Accepted Answer

To avoid dividing by zero in the original equation.

Question 9

Given $$\frac{x+3}{x-1} = 2$$, what is the restriction for $$x$$?

Accepted Answer

$$x 
eq 1$$

Question 10

A medical dosage formula is given by $$D = \frac{500}{w-10}$$, where $$w is $$the patient's weight in kg. For which value of $$w is $$the formula undefined?

Accepted Answer

$$w = 10$$

Question 11

Solve the equation $$\frac{3x}{x+2} = 6. $$What is the solution?

Accepted Answer

$$x = 4$$

Question 12

If you solve $$\frac{x+2}{x-3} = 1$$, what must you check before accepting your solution?

Accepted Answer

That $$x 
eq 3$$

Question 13

A chemical reaction rate is modeled by $$R = \frac{100}{t-5}$$, where $$t is $$time in seconds. What is the restriction for $$t$$?

Accepted Answer

$$t 
eq 5$$

Question 14

Solve the equation $$\frac{x-1}{x+1} = 2. $$What is the solution?

Accepted Answer

$$x = 3$$

Question 15

Which of the following is NOT a valid step in solving rational equations?

Accepted Answer

Ignore restrictions and accept all solutions.

Question 16

Solve the equation $$\frac{2x+3}{x-4} = 5. $$What is the solution?

Accepted Answer

$$x = 5.75$$

Question 17

If a solution to a rational equation makes the denominator zero, what should you do?

Accepted Answer

Exclude the solution from the solution set.

Question 18

Solve the equation $$\frac{x+2}{x-2} = 4. $$What is the solution?

Accepted Answer

$$x = 2.67$$

Question 19

Which real-world scenario could be modeled by a rational equation?

Accepted Answer

Calculating the speed of a car using $$v = d/t$$ where $$t$$ cannot be zero.

Question 20

Solve the equation $$\frac{x-3}{x+2} = 1. $$What is the solution?

Accepted Answer

$$x = 5$$

Solving Rational Equations

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