How Do You Continue Long Division with the Expression \((\sqrt{x} + \delta)/x\)?

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The discussion centers on the mathematical expression \((\sqrt{x} + \delta)/x\) and the challenges of performing long division with it. The user initially simplifies the expression to \(\sqrt{x}\) and encounters difficulty with the remainder \(-\delta\sqrt{x}\). A participant suggests that traditional division yields \(\frac{1}{\sqrt{x}} + \frac{\delta}{x}\), indicating that this approach does not simplify the problem further. The conversation highlights the complexities of manipulating algebraic expressions involving square roots and variables.

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I am trying to solve the following problem:

$$(\sqrt{x} + \delta)/x$$

Using long division, I get:

$$\sqrt{x}$$

On top and I end up with

$$-\delta\sqrt{x}$$

On the bottom and am unsure how to proceed from there? I'm sorry I can't write out all my work out as I'm not sure how I could format it properly with LaTeX. Any advice would be appreciated.
 
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TKline007 said:
I am trying to solve the following problem:

$$(\sqrt{x} + \delta)/x$$

Using long division, I get:

$$\sqrt{x}$$

On top and I end up with

$$-\delta\sqrt{x}$$

On the bottom and am unsure how to proceed from there? I'm sorry I can't write out all my work out as I'm not sure how I could format it properly with LaTeX. Any advice would be appreciated.

what exactly is the problem you are working on that involves the quotient \frac{\sqrt{x} + \delta}{x} ?

division (not long) yields \frac{1}{\sqrt{x}} + \frac{\delta}{x}, and offers nothing more simple than what you started with ...
 

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