Understanding and Solving Rational Equations

The video tutorial explains how to solve a rational equation involving negative exponents. It begins with an introduction to the equation and the properties of negative exponents. The tutorial then demonstrates how to eliminate fractions by multiplying through by a common term, leading to a quadratic equation. The quadratic is factored using the grouping method, and solutions are found using the zero product property. Both solutions are verified for correctness. The video concludes with a summary and offers additional resources for further practice.

What is the equivalent expression for x raised to the negative second power?

• 2x

• x^-2

• 1/x^2

• x^2

What is the first step in solving the equation x^-2 + x^-1 = 20?

• Divide by x

• Multiply every term by x^2

• Subtract x from both sides

• Add 20 to both sides

After eliminating fractions, what form does the equation take?

• x + 1 = 20x

• x^2 - x = 20

• 1 + x = 20x^2

• x^2 + x = 20x^2

What is the next step after obtaining the equation 0 = 20x^2 - x - 1?

• Multiply by x

• Add 1 to both sides

• Factor the trinomial

• Use the quadratic formula

Which pair of numbers multiply to -20 and add to -1?

• -4 and -5

• 4 and -5

• -4 and 5

• 4 and 5

What is the result of factoring 20x^2 - x - 1?

• (4x + 1)(5x - 1)

• (4x - 1)(5x + 1)

• (5x + 1)(4x - 1)

• (5x - 1)(4x + 1)

What is the value of x when solving 4x - 1 = 0?

• -4

• 4

• 1/4

• -1/4

What is the value of x when solving 5x + 1 = 0?

• 1/5

• -1/5

• 5

• -5

Which of the following is a correct solution for the original equation?

• x = -1/4

• x = 1/4

• x = -1/2

• x = 1/2

What should you do if you want more practice problems on rational equations?

• Rewatch the video

• Check the description for links

• Ask a friend

• Search online