Rational Equations and Graphing Techniques

The video tutorial covers solving rational equations by first identifying values that make denominators zero, finding the least common denominator, and clearing fractions. Two examples are solved, with solutions verified graphically using a calculator. The process involves converting fractions to decimals and adjusting graphing windows to find intersection points, ensuring solutions are correct.

What is the first step in solving a rational equation?

• Graph the equation

• Identify values of x that make denominators zero

• Solve for x

• Identify the common denominator

In the first example, why can't x equal 4?

• It makes the equation too complex

• It results in division by zero

• It is not a real number

• It is not an integer

What is the solution for x in the first example?

• x = 11

• x = 35/3

• x = 4

• x = 23

How is the solution for the first example verified graphically?

• By calculating the area under the curve

• By finding the point of intersection

• By comparing with a table of values

• By checking the slope of the line

In the second example, which values of x are not allowed?

• x = 2 and x = 5

• x = -4 and x = 3

• x = 0 and x = 1

• x = -3 and x = 4

What is the least common denominator in the second example?

• x + 4 and x - 3

• x - 3

• x + 4

• x - 4

What is the solution for x in the second example?

• x = 5

• x = 2

• x = 7

• x = -34/5

How is the solution for the second example verified graphically?

• By comparing with a table of values

• By calculating the area under the curve

• By finding the point of intersection

• By checking the slope of the line

What is the decimal approximation of -34/5?

• -7.8

• -6.8

• -6.5

• -7.5

What is the purpose of using a graphing calculator in these examples?

• To simplify the equation

• To find the common denominator

• To verify the solution

• To solve the equation