Rational Equations and Their Solutions

The video tutorial covers solving rational equations by finding the least common denominator (LCD), factoring expressions, and simplifying problems. The instructor corrects a mistake in the problem setup and demonstrates solving a quadratic equation. The importance of checking solutions for extraneous values is emphasized, ensuring they do not make the denominator zero.

What was the initial problem setup in the video?

• x + 2 = 4

• x^2 - x = 0

• x + 2id x - 4

• x^2 + 2x = 4

What is the main goal when solving rational equations?

• To add fractions

• To get variables off the denominator

• To find the numerator

• To simplify the numerator

What is the first step in solving rational equations with variables in the denominator?

• Add all terms

• Divide all terms

• Factor anything that can be factored

• Subtract all terms

What is the Least Common Denominator (LCD) for the problem x^2 - 1?

• x^2 - 1

• x - 1

• x * (x - 1) * (x + 1)

• x + 1

What happens when you multiply every term by the LCD?

• The terms get added

• The denominators cancel out

• The numerators cancel out

• The terms get subtracted

What was the corrected problem setup?

• x^2 - x

• x^2 + 2x

• x + 2 = 4

• x^2 - 1

What is the simplified form of the equation after applying the LCD?

• x^2 - x = 0

• x^2 + x - 2 - 4x = -2

• x^2 - 3x = 0

• x^2 + 2x = 4

What are the solutions to the equation x^2 - 3x = 0?

• x = 4 and x = -1

• x = 2 and x = 1

• x = 1 and x = 0

• x = 3 and x = 0

What must you do after finding the solutions to the equation?

• Subtract them

• Add them together

• Multiply them

• Check if they make the denominator zero

What is the term used for solutions that make the denominator zero?

• Valid

• Extraneous

• Invalid

• Redundant