Rational Equations and Graphing Concepts

The video tutorial covers solving rational equations by first identifying values that make the denominator zero and excluding them. It explains clearing fractions using a common denominator, solving the equation, and verifying solutions through graphing. The tutorial includes two examples, highlighting the importance of checking solutions graphically to ensure accuracy.

What is the first step in solving a rational equation?

• Multiply both sides by zero

• Identify values of x that make the denominator zero

• Add fractions to both sides

• Subtract the numerator from the denominator

What is the least common denominator for the denominators 12 and 4?

• 4

• 16

• 12

• 48

After clearing the fractions in the first example, what is the next step?

• Multiply both sides by 2

• Add 7 to both sides

• Divide both sides by 3

• Subtract 3x from both sides

How do you verify the solution of a rational equation using graphing?

• Find the point of intersection

• Find the y-intercept

• Find the x-intercept

• Find the slope of the line

What is the decimal equivalent of 31/2?

• 14.5

• 13.5

• 16.5

• 15.5

In the second example, what value of x must be excluded?

• x = 5

• x = 10

• x = -5

• x = 0

What is the common denominator in the second example?

• x + 5

• x + 10

• x - 5

• x - 10

What is the solution for x in the second example?

• x = 3

• x = -3

• x = 10/3

• x = -10/3

What is the decimal value of -10/3?

• -3.33

• -3.3333

• -3.3

• -3.333

How do you verify the solution of the second example using graphing?

• Find the x-intercept

• Find the y-intercept

• Find the point of intersection

• Find the slope of the line