Solving for n: Natural Number Fraction Equality

[Shooting Star]

Ah, ok, I'll try not to say that much next time. How 'bout this?

A newbie not so good in Math may get confused. Perhaps the best would be to give him just the first step of your derivation; or something like

$\frac{n^{2} - n + 2}{n + 1}$ = $\frac{n(n+1) - 2n + 2}{n + 1}$, so that he again makes a factor of (n+1) from the rest of the terms in the numerator.

It all depends on how it's going.

 

[HallsofIvy]

A newbie not so good in Math may get confused. Perhaps the best would be to give him just the first step of your derivation; or something like

$\frac{n^{2} - n + 2}{n + 1}$ = $\frac{n(n+1) - 2n + 2}{n + 1}$, so that he again makes a factor of (n+1) from the rest of the terms in the numerator.

It all depends on how it's going.

I doubt that would help him much
$$\frac{n^2- n+ 2}{n+1}= \frac{(n-2)(n+1)+ 4}{n+1}$$
would be much better.
Of course, it would be best if he learned to divide!

 

[Theofilius]

Ok. I understand now, thanks everyone.
$$n^2- n+ 2= (n-2)(n+1)+4$$

So i divide the whole equation with $$\frac{1}{n+1}$$

$$\frac{n^2-n+2}{n+1}= n-2 + \frac{4}{n+1}$$

So only for n=1 and n=3, I get natural numbers for the fraction, right?

 

[tiny-tim]

So only for n=1 and n=3, I get natural numbers for the fraction, right?

That's it!

So just remember the moral - turn any nasty fraction into a nice one! (and practise your multiplication …)

 

[Shooting Star]

... or something like

$\frac{n^{2} - n + 2}{n + 1}$ = $\frac{n(n+1) - 2n + 2}{n + 1}$, so that he again makes a factor of (n+1) from the rest of the terms in the numerator.

It all depends on how it's going.

I doubt that would help him much
$$\frac{n^2- n+ 2}{n+1}= \frac{(n-2)(n+1)+ 4}{n+1}$$
would be much better.

It depends, I repeat, on how you feel the student is responding. I want to give a hint, not the answer. He may miss the point even if you give the hint your way, as happened in this thread.

When you divide (n^2-n+2) by (n+1), what is the quotient and the remainder? .

Of course, it would be best if he learned to divide!

Ah, somebody who finally agrees with me. But I was considered dated. Division takes care of all the problems.

And, as you have already been told, your fraction is the same as 1+ 10/(n-3).

I think a perusal of the complete thread is necessary before posting; otherwise OPs may get confused.

 

[tiny-tim]

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