Solving Rational Equations and Expressions

In this video tutorial, the teacher demonstrates how to solve rational equations by first identifying domain restrictions. The process involves setting each denominator equal to zero to find values that x cannot equal. The teacher then explains how to make all denominators uniform by multiplying them with necessary factors. Once the denominators are the same, they are dropped, and the numerators are simplified. The teacher distributes and combines terms to solve for x, resulting in a solution of x = 27/4.

What is the first step in solving rational equations?

• Find the common denominator

• Identify domain restrictions

• Multiply by the reciprocal

• Add fractions

How do you find domain restrictions for a rational equation?

• Set the numerator equal to zero

• Add the denominators

• Multiply both sides by zero

• Set the denominator equal to zero

What is the domain restriction for the denominator x + 4?

• x cannot equal 2

• x cannot equal 0

• x cannot equal -4

• x cannot equal 4

Why do we multiply the numerator and denominator by the same factor?

• To eliminate variables

• To simplify the equation

• To change the equation

• To keep the equation balanced

What should you do once all denominators look the same?

• Divide them by a variable

• Add them together

• Drop them and focus on the numerators

• Multiply them by a constant

What is the result of distributing 7 in the expression 7(x - 2)?

• 14x - 7

• 7x - 14

• 14x + 7

• 7x + 14

How do you combine like terms in the expression 7x - 3x?

• 4x

• 10x

• 3x

• 7x

What is the next step after combining like terms in an equation?

• Divide both sides by a constant

• Subtract a constant from both sides

• Multiply both sides by a variable

• Add a constant to both sides

What is the value of x in the equation 4x = 27?

• x = 27

• x = 4/27

• x = 4

• x = 27/4

What is the final step in solving the equation 4x = 27?

• Divide both sides by 4

• Multiply both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides