What about write each quadratic equation in standard form 4/x + 10 = 4/x-1

To write the equation \(\frac{4}{x} + 10 = \frac{4}{x-1}\) in standard form, follow these steps:

1. **Eliminate the fractions** by multiplying every term by the least common denominator (LCD). In this case, the LCD is \(x(x - 1)\):

   \[
   x(x - 1) \left(\frac{4}{x} + 10\right) = x(x - 1) \left(\frac{4}{x-1}\right)
   \]

2. **Distribute and simplify** each side:
   
   On the left side:
   \[
   (x - 1) \cdot 4 + 10 \cdot x(x - 1)
   \]

   On the right side:
   \[
   4 \cdot x
   \]

   So, you get:
   \[
   4x - 4 + 10x^2 - 10x = 4x
   \]

3. **Simplify** and move all terms to one side to set the equation to zero:

   Subtract \(4x\) from both sides:
   \[
   10x^2 - 10x - 4 = 0
   \]

4. **Simplify the coefficients** if possible:

   Divide the entire equation by 2 to simplify it:
   \[
   5x^2 - 5x - 2 = 0
   \]

The equation \(5x^2 - 5x - 2 = 0\) is now in standard form.

Would you like more details on any of these steps or have any other questions?

Here are five related questions:
1. How do you find the roots of a quadratic equation?
2. What does it mean for a quadratic equation to be in standard form?
3. How can you complete the square for a quadratic equation?
4. What are the applications of quadratic equations in real life?
5. How do you determine the axis of symmetry for a quadratic equation?

**Tip:** Always simplify the coefficients if possible after arranging the equation in standard form to make solving easier.

Learn how to write the quadratic equation 4/x + 10 = 4/x-1 in standard form with detailed steps. This problem covers algebraic concepts such as fraction operations and quadratic equation formulas. Suitable for students in Grades 10-12.

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