Solving Rational Equations Effectively

What is the first step in solving rational equations?

• Add the denominators

• Multiply both sides by the denominator

• Subtract the denominators

• Divide both sides by the numerator

What operation is primarily used to solve rational equations?

• Subtraction

• Multiplication

• Division

• Addition

Why is it important to check for extraneous solutions in rational equations?

• To ensure the solution does not cause division by zero

• To make the equation simpler

• To convert the rational equation into an integer equation

• To find more solutions

How do you determine if a solution is extraneous?

• By dividing it by the numerator

• By substituting it back into the original equation

• By multiplying it with the denominator

• By adding it to the original equation

If Arthur and Cheyenne can paint a wall together in 6 hours, and Cheyenne works twice as fast as Arthur, how long does it take Cheyenne to paint the wall alone?

• 18 hours

• 3 hours

• 12 hours

• 9 hours

In the work rate problem, what is the relationship between Cheyenne's and Arthur's work rates?

• There is no relationship mentioned

• Cheyenne works twice as fast as Arthur

• Cheyenne works at the same rate as Arthur

• Cheyenne works half as fast as Arthur

What defines an extraneous solution in the context of rational equations?

• A solution that simplifies the equation

• A solution that makes the equation a perfect square

• A solution derived from incorrect operations

• A solution that, when substituted back into the original equation, does not hold true

What is the purpose of finding a common denominator in rational equations?

• To simplify the equation

• To eliminate the denominators

• To find the extraneous solutions

• To multiply the numerators

What is the speed of the river's current if Jake paddles 16 miles downstream in the same time it takes to paddle 6 miles upstream?

• 2 miles per hour

• 3 miles per hour

• 5 miles per hour

• 4 miles per hour

What equation represents the time it takes to paddle upstream and downstream in the river problem?

• Distance = Rate × Time

• Time = Distance + Rate

• Time = Distance / Rate

• Rate = Distance / Time