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

In summary, the conversation involves trying to solve a problem involving the quotient $$(\sqrt{x} + \delta)/x$$ using long division. The result is $$\sqrt{x}$$ on the top and $$-\delta\sqrt{x}$$ on the bottom. However, the speaker is unsure of how to proceed from there and is seeking advice.
  • #1
TKline007
1
0
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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  • #2
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 [tex]\frac{\sqrt{x} + \delta}{x}[/tex] ?

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

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

What is long division with variables?

Long division with variables is a method of dividing algebraic expressions that contain variables. It is similar to long division with numbers, but instead of dividing numbers, we divide expressions with variables.

Why is long division with variables important?

Long division with variables is important because it allows us to simplify and solve complex algebraic expressions. It is a fundamental skill in algebra and is often used in higher level math courses such as calculus and linear algebra.

How do I perform long division with variables?

To perform long division with variables, follow these steps:1. Arrange the expression in descending order of the variable.2. Divide the first term of the dividend by the first term of the divisor.3. Multiply the quotient by the divisor and subtract it from the dividend.4. Bring down the next term of the dividend.5. Repeat the process until there are no more terms to bring down.6. The final quotient is the answer.

Can long division with variables be used to solve equations?

Yes, long division with variables can be used to solve equations. It allows us to simplify and rearrange equations by dividing both sides by the same expression. This can help us solve for the value of the variable.

Are there any special cases in long division with variables?

Yes, there are special cases in long division with variables. One example is when the leading coefficient of the divisor is not 1. In this case, we have to multiply the divisor by the leading coefficient of the dividend before starting the division process. There are also special cases when dealing with fractions and negative exponents.

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