Breaking a fraction down to a sum of fractions

[kylera]

Homework Statement

Re-write the following fraction into the sum of fractions:
1/[(n^3)+n]

Homework Equations

None that I can think of. . .

The Attempt at a Solution

I first changed [(n^3)+n] to n[(n^2)+1], so by the rules, the aformentioned fraction should equate to (A/n) + (B/[(n^2)+1]). That means A * [(n^2)+1] + B * n should equate to 1. This is where I run into problems. Since there's only one n^2, that means A should equate to zero. However, there's also the constant A, which should equate to one. 0 doesn't equate to one. Is the problem faulty or am I missing something?

 

[Defennder]

If the quadratic term in the denominator cannot be decomposed into linear factors, then the numerator should be given the form Ax+B instead, rather than just A.

 

[spideyunlimit]

1/[(n^3)+n] = 1 / (n)(n^2 + 1)
= 1 + n^2 - n^2 / (n)(n^2 + 1)
= (1/n) - [n/(n^2 +1)]

 

[spideyunlimit]

@poster - the method u used is only valid for two linear expressions' product, but for your one you'll have to use Bn instead of just B.

 

[kylera]

ARGH! Totally forgot that! Thanks!