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.