Solving Rational Equations with LCD Techniques

Why can't cross multiplication be used for the equations discussed?

• Because cross multiplication only works with linear equations

• Because the equations do not contain any fractions

• Because there are more than two fractions in the equation

• Because there is only one fraction in the equation

What is the least common denominator (LCD) used in the first example?

• 4X

• 3X

• 2X

• 5X

What does multiplying the numerators by the LCD accomplish?

• It simplifies the equation to a quadratic form

• It reduces the equation to a single fraction

• It converts the rational equation into an exponential equation

• It eliminates the fractions from the equation

Why is the LCD method preferred over cross multiplication in these examples?

• It simplifies the equation to avoid large powers of X

• It directly provides the solution without further steps

• It requires less algebraic manipulation

• It only works with linear equations

What is the result after applying the LCD method to the first equation?

• X = 8

• X = -8

• 7X = -36

• 7X = -56

What is the final solution for the first equation?

• X = -7

• X = -8

• X = 7

• X = 8

What step follows after applying the LCD and simplifying the equation?

• Graphing the equation

• Factoring the polynomial

• Solving the resulting linear equation

• Cross multiplying the remaining terms

Why is it important to check for extraneous solutions?

• To ensure the solution does not result in division by zero

• To confirm the solution is a fraction

• To verify the solution is a positive number

• To make sure the solution is not a rational number

What is the LCD in the second example?

• 2X

• 3X

• 4X

• 5X

What is the final solution for the second equation?

• X = 2

• X = -3

• X = 3

• X = -2