Silly question but need clarity

[mathsnoob94]

I have a question regarding simplify algebra in a fraction. I can not find any similar examples. An example of what I am talking about:

\(\displaystyle \frac{100x^2 + 30x - 20}{10x}\)

The 10x being the bottom of the fraction.

Is the answer

10x + 3 - 2/x ?

 

[HallsofIvy]

Yes, of course. \(\displaystyle \frac{a+ b+ c}{d}= \frac{a}{d}+ \frac{b}{d}+ \frac{c}{d}\).

 

[Deleted member 4993]

I have a question regarding simplify algebra in a fraction. I can not find any similar examples. An example of what I am talking about:

100x^2 + 30x - 20
10x

The 10x being the bottom of the fraction.

Is the answer

10x + 3 - 2/x ?

Exactly where do you need clarity? How did you get the "answer"? Is there any step in your work - that you did not understand?

It is very IMPORTANT that you are clear about the process of this problem. You will use "these steps" many many times later. It is very good that you "demanded" clarity.

Keep up the good work - and keep asking questions.

By the way, your answer is CORRECT!!

 

[Dr.Peterson]

I have a question regarding simplify algebra in a fraction. I can not find any similar examples. An example of what I am talking about:

\(\displaystyle \frac{100x^2 + 30x - 20}{10x}\)

The 10x being the bottom of the fraction.

Is the answer

10x + 3 - 2/x ?

One reason you may be having trouble finding similar examples is that, given a fraction like this, there are two very different things you can do. To simplify it as a fraction, you would divide the numerator and denominator by any common factors, resulting in a simpler fraction; this one can't be simplified in that sense. What you have done is to carry out the division, which in the case of a monomial divisor means just dividing each term by that divisor, as you have done.

The difference is like saying 18/4 simplifies to the fraction 9/2, or to the mixed number 4 1/2. Both are valid, but they aim at different goals, and they would be in different chapters of a textbook (rational expressions vs. operations on polynomials).

 

[lookagain]

Yes, of course. \(\displaystyle \frac{a+ b+ c}{d}= \frac{a}{d}+ \frac{b}{d}+ \frac{c}{d}\).

Which side above in the quote box would be considered simplified? The right-hand
side has all like terms. I would move from the right-hand side and simplify to the left-hand side.

 

[Dr.Peterson]

One reason you may be having trouble finding similar examples is that, given a fraction like this, there are two very different things you can do. To simplify it as a fraction, you would divide the numerator and denominator by any common factors, resulting in a simpler fraction; this one can't be simplified in that sense. What you have done is to carry out the division, which in the case of a monomial divisor means just dividing each term by that divisor, as you have done.

The difference is like saying 18/4 simplifies to the fraction 9/2, or to the mixed number 4 1/2. Both are valid, but they aim at different goals, and they would be in different chapters of a textbook (rational expressions vs. operations on polynomials).

I misspoke in saying this couldn't be simplified as a fraction; of course you can divide everything by 10. Since both goals make sense, we really need to see the actual wording of the problem you are working on, and its context.