simplify (x+h) - (x)  x = square root of x and h is not equal to 0

To simplify the expression \((\sqrt{x+h}) - (\sqrt{x})\), where \(x = \sqrt{x}\) and \(h \neq 0\), follow these steps:

1. **Expression:** \((\sqrt{x+h}) - (\sqrt{x})\)

2. This expression is already in its simplest form. However, if you're interested in the difference between the square roots, you can rationalize the denominator by multiplying the numerator and the denominator by the conjugate:

\[
\frac{(\sqrt{x+h}) - (\sqrt{x})}{1} \cdot \frac{(\sqrt{x+h}) + (\sqrt{x})}{(\sqrt{x+h}) + (\sqrt{x})}
\]

3. Multiply both numerator and denominator:

\[
\frac{(\sqrt{x+h})^2 - (\sqrt{x})^2}{(\sqrt{x+h}) + (\sqrt{x})}
\]

4. Simplify the numerator using the difference of squares:

\[
\frac{(

Learn how to simplify the expression (sqrt(x+h)) - (sqrt(x)), where x = sqrt(x) and h ≠ 0. Follow step-by-step instructions and understand the difference of squares formula used in the process. Suitable for high school students studying algebra and square roots.

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