       Re: Combining Fractions with Identical Denominator?

• To: mathgroup at smc.vnet.net
• Subject: [mg81043] Re: Combining Fractions with Identical Denominator?
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Sun, 9 Sep 2007 06:12:17 -0400 (EDT)
• References: <fbqq2m\$6p4\$1@smc.vnet.net>

```On 7 sep, 08:11, "Jung-Tsung Shen" <jus... at gmail.com> wrote:
> I have a sum of a series of fractions (symbolic) of about 50 terms.
> How can I have Mathematica to sum up those with the same denominator?
> By inspection, there are about 5 different denominators. I have wrote
> a simple rule to compare the denominator term by term, but it's rather
> slow. Moreover, sometimes the denominators differ only with a +/-
> sign, a numerical factor (say, 1/2), or a complex i.
>
> In mathematical terms, I have a series in the following form (the
> number of terms can vary):
>
> N1/D1 + N2/D2 + ... + N50/D50
>
> These Di's form 5 different groups. Within each group, there are
> proportional to each other. How could I sum up this series such that
> those terms with Di in the same group is summed?
>
> Thanks for any input.
>
> JT

Good day,

I would use "Collect" this way (example):

In:=ff = n1/(d1 + d2) + n2/d3 + n3/(2*d3) + (n4 + n5)/(I*(d1 +
d2));

In:=dd = List @@ Denominator[Together[ff]]

Out={2, d1 + d2, d3}

In:=Collect[ff, dd]

Out=(n2 + n3/2)/d3 + (n1 - I*(n4 + n5))/(d1 + d2)

V.Astanoff

```

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