make  s the fubject of the formula : x= square root of s-a/s-b

To make \( s \) the subject of the formula \( x = \sqrt{\frac{s-a}{s-b}} \), follow these steps:

1. Start with the given equation:
   \[
   x = \sqrt{\frac{s-a}{s-b}}
   \]

2. Square both sides to eliminate the square root:
   \[
   x^2 = \frac{s-a}{s-b}
   \]

3. Multiply both sides by \( s - b \) to clear the fraction:
   \[
   x^2(s - b) = s - a
   \]

4. Distribute \( x^2 \) on the left side:
   \[
   x^2s - x^2b = s - a
   \]

5. Collect all terms involving \( s \) on one side of the equation:
   \[
   x^2s - s = x^2b - a
   \]

6. Factor \( s \) out from the left side:
   \[
   s(x^2 - 1) = x^2b - a
   \]

7. Solve for \( s \) by dividing both sides by \( x^2 - 1 \):
   \[
   s = \frac{x^2b - a}{x^2 - 1}
   \]

So, the subject of the formula \( s \) is:
\[ 
s = \frac{x^2b - a}{x^2 - 1} 
\]

Do you want more details or have any questions?

Here are 5 numbered questions for you to ask:
1. How do you eliminate square roots in an equation?
2. What is the process for isolating a variable in a fraction?
3. Can you explain how to factor out a common term?
4. How do you handle equations with multiple variables?
5. What are the properties of exponents used in solving equations?

**Tip:** When dealing with equations involving square roots, always consider the domain of the variable to ensure the solution is valid within the given constraints.

Learn how to solve for s in the equation x = sqrt((s-a)/(s-b)) with a detailed step-by-step solution. This problem covers key algebraic concepts, including square roots and fraction simplification. Suitable for students in Grades 9-12.

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