How to solve a rational equation

The video tutorial covers solving algebraic equations with variable denominators by finding the least common multiple (LCM). It demonstrates multiplying expressions, simplifying them, and solving quadratic equations. The instructor explains factoring techniques and applies the zero-product property to find solutions. The tutorial emphasizes understanding each step and encourages questions for clarity.

What is the least common multiple (LCM) of the expressions x and x + 7?

• x + 7

• x^2 + 7

• x(x + 7)

• x^2 + 7x

When multiplying through by the LCM, what is the resulting expression for 3x + 25?

• 3x + 25x

• 3x(x + 7)

• 3x^2 + 25x

• 3(x + 7)

What is the simplified form of the quadratic equation obtained after removing the denominators?

• 3x^2 - 5x^2 + 25x - 35 = 0

• 3x^2 + 25x - 5x^2 = 3x + 21

• 3x^2 - 5x^2 + 25x - 35 = 3x + 21

• 3x^2 + 25x - 5x^2 - 35 = 3x + 21

What is the first step in solving the quadratic equation 2x^2 + 13x + 21 = 0?

• Add 13x to both sides

• Subtract 21 from both sides

• Factor the equation

• Divide by 2

Which of the following pairs of factors correctly factorizes the quadratic equation 2x^2 + 13x + 21?

• (2x + 21)(x + 1)

• (2x + 3)(x + 7)

• (2x + 1)(x + 21)

• (2x + 7)(x + 3)

What are the solutions to the equation 2x^2 + 13x + 21 = 0 after applying the zero-product property?

• x = -7 and x = -3/2

• x = 7 and x = 3/2

• x = -7/2 and x = -3

• x = 7/2 and x = 3

Why is it beneficial to eliminate the negative sign in front of the quadratic equation before factoring?

• It simplifies the equation

• It makes the equation easier to solve

• It ensures the leading coefficient is positive

• It reduces calculation errors