       Combining Fractions with Identical Denominator?

• To: mathgroup at smc.vnet.net
• Subject: [mg80994] Combining Fractions with Identical Denominator?
• From: "Jung-Tsung Shen" <jushen at gmail.com>
• Date: Fri, 7 Sep 2007 02:07:34 -0400 (EDT)

```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

```

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