How to you convert this equation to the standard quadratic form? [4 + (1/x) - (1/(x^2)) = 0]

To convert the equation \( 4 + \frac{1}{x} - \frac{1}{x^2} = 0 \) to the standard quadratic form, follow these steps:

1. **Multiply through by \( x^2 \)** to eliminate the denominators. This will give us a quadratic equation in terms of \( x \).

   \[
   x^2 \left( 4 + \frac{1}{x} - \frac{1}{x^2} \right) = 0
   \]

   Distribute \( x^2 \) across all the terms:

   \[
   4x^2 + x - 1 = 0
   \]

2. **Resulting quadratic equation** is now in the standard form \( ax^2 + bx + c = 0 \), where:
   - \( a = 4 \)
   - \( b = 1 \)
   - \( c = -1 \)

So, the equation in standard quadratic form is:

\[
4x^2 + x - 1 = 0
\]

Would you like more details or have any questions? Here are some related questions for further practice:

1. How do you solve the quadratic equation \( 4x^2 + x - 1 = 0 \)?
2. What is the quadratic formula, and how can it be used to solve this equation?
3. Can you factor \( 4x^2 + x - 1 = 0 \)?
4. How do you find the discriminant of a quadratic equation?
5. What are the solutions of a quadratic equation when the discriminant is negative, zero, or positive?

**Tip**: Always check for ways to simplify expressions or multiply through by a variable to eliminate fractions before converting to standard quadratic form.

How do you convert this equation to the standard quadratic form? [4 + (1/x) - (1/(x^2)) = 0]

Learn how to convert the equation 4 + (1/x) - (1/(x^2)) = 0 into the standard quadratic form. This tutorial covers algebraic manipulation of rational expressions, focusing on multiplying to eliminate fractions. Ideal for students in Grades 9-10.

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