How do you divide e^x by 1+x?

Question

So apparently to find the first four terms of a Maclauren series, I have to divide the numerator, which is e^x, by the denominator, which is 1+x. How do you divide them? When I divided them with the way I think im supposed to divide them, I get e^x+xe^x+x^2e^x+x^3e^x...

Raffaele · Accepted Answer

Trascendent functions cannot be divided by algebraic functions
Mac Laurin series for (e^x)/(1 + x) begins in this way
1 + x^2/2 - x^3/3 + (3 x^4)/8 - (11 x^5)/30 +...

In the second part of you question you multiply e^x by
1 + x + x^2 + x^3 + x^4 ... whose sum is 1/(1 - x)

If you want to do this way, you have to use
1 - x + x^2 - x^3 ... whose sum is 
1/(1 + x)

Anyway, I wrote some derivatives of e^x/(x + 1)
in the case you wanted to apply Mac Laurin series directly

e^x/(1 + x)
(x e^x)/(1 + x)^2
(e^x (1 + x^2))/(1 + x)^3
(e^x (-2 + 3 x + x^3))/(1 + x)^4
(e^x (9 - 8 x + 6 x^2 + x^4))/(1 + x)^5
...

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How do you divide e^x by 1+x?

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