Solving Rational Equations Concepts

The video tutorial covers solving rational equations, starting with linear equations with fractions. It explains how to eliminate fractions by using the least common multiple and solve equations with variables in the denominator. The tutorial also highlights the importance of recognizing excluded values and extraneous solutions to avoid errors in solving rational equations.

What is the first step in solving a rational equation with fractions?

• Add all fractions together

• Divide by the largest denominator

• Find the least common multiple of the denominators

• Subtract the numerators

What is the least common multiple of 15, 6, and 5?

• 15

• 90

• 60

• 30

When multiplying each term by the least common multiple, what happens to the fractions?

• They remain unchanged

• They become larger

• They are eliminated

• They are added together

What is the solution to the equation 2X/15 - 1/6 = X/5 after eliminating the fractions?

• X = 5/2

• X = -5/2

• X = 2/5

• X = -2/5

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CCSS.HSA.REI.A.2

What is the main idea when solving rational equations with variables in the denominator?

• To divide by the largest variable

• To subtract the variables

• To find the least common denominator

• To add the variables together

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CCSS.HSA.REI.A.2

In the equation 5/(X-3) = 4/(X+2), what should you multiply both sides by to eliminate the denominators?

• 5

• X - 3

• X + 2

• (X - 3)(X + 2)

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CCSS.HSA.REI.A.2

How do you clear the parentheses when solving rational equations with variables?

• By dividing each term inside by the outside term

• By subtracting the terms inside

• By multiplying each term inside by the outside term

• By adding the terms inside

What is the result of solving the equation 5X + 10 = 4X - 12?

• X = -12

• X = 12

• X = -22

• X = 22

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CCSS.HSA.REI.A.2

Why is it important to be aware of excluded values in rational equations?

• They can make the equation easier to solve

• They simplify the equation

• They can lead to division by zero

• They are always the correct solutions

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CCSS.HSA.REI.A.2

What are extraneous solutions in the context of rational equations?

• Solutions that simplify the equation

• Solutions that are always correct

• Solutions that make the equation more complex

• Solutions that are excluded due to division by zero

Tags

CCSS.HSA.REI.A.2