Rational Equations and Expressions

The video tutorial covers solving rational expressions by building on previous lessons about adding and subtracting fractions. It explains the process of eliminating fractions by multiplying by the least common denominator (LCD) and extends this method to rational equations with variables in the denominator. The tutorial emphasizes the importance of checking solutions against constraints to ensure they are valid, particularly focusing on avoiding zero in the denominator.

What is the first step in solving rational expressions?

• Get rid of the fractions

• Divide the fractions

• Subtract the fractions

• Add the fractions

In the example problem, what is the least common denominator (LCD) of 3, 4, and 6?

• 6

• 12

• 18

• 24

What do you do after finding the LCD in a fraction problem?

• Add the numerators

• Multiply everything by the LCD

• Subtract the denominators

• Divide by the LCD

When solving rational equations, what additional challenge is introduced?

• More complex numerators

• Variables in the denominator

• Larger numbers

• Multiple solutions

What is the LCD for the example problem with 3x in the denominator?

• 3x

• 6x

• x

• 3

What is the result of multiplying 3 times 2 in the example problem?

• 5

• 8

• 6

• 7

After simplifying the equation, what is the value of x?

• 5

• 3

• 2

• 4

What value can x not be in the given problem?

• 1

• 2

• 3

• 0

Why can't x be zero in the problem?

• It would make the LCD zero

• It would make the equation unsolvable

• It would make the denominator zero

• It would make the numerator zero

What should you do after solving the equation to ensure the solution is correct?

• Check the constraints

• Recalculate the LCD

• Add the fractions again

• Multiply the solution by the LCD