[Rafael-SOWNet]

When one side of a quotient is a sum, and every term holds a polynomial factor of the other side, as it is or to a whole power, that factor now comes out of the sum before the factors are paired off.

Simplify	master and 2.6.0	now
(x * (y + 1) + (y + 1)^2) / (y + 1)^4	left as it is	(x + y + 1) / (y + 1) ^ 3
(x * (x^2 + 1) + (x^2 + 1)^2) / (x^2 + 1)^4	left as it is	(x ^ 2 + 1 + x) / (x ^ 2 + 1) ^ 3
(a * (x^2 + 1) + b * (x^2 + 1)^2) / (x^2 + 1)^3	expanded, over x ^ 4 + 2 * x ^ 2 + 1	(a + b * (x ^ 2 + 1)) / (x ^ 2 + 1) ^ 2

• The rules take k out of k*p + k*q, but not out of k*p + k^n. So only the first-power case cancelled.
• The quotient rule squares the denominator at each derivative. So the derivatives of e^x / (1 + x^2), simplified step by step, went 21, 149, 629 and 5,117 nodes. They now go 21, 69, 109 and 149. A Taylor expansion to 9 terms took 8 s and takes 1 s, with the same coefficients.
• Polynomial factors only. Taking a power of sin(t) out first left Simplify() does not handle complex trigonometrical statements well #557's second expression one Simplify short of 0. That case has its own route to cancellation, through the opened angles. DoubleAngleOverSineTest caught it.
• Three of the new tests fail on master. The suite, the trio, F#, AOT and the eight harnesses pass.

Fixes #2301.

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.77%. Comparing base (aef5535) to head (2e1ef0d).

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@@           Coverage Diff           @@
##           master    #2306   +/-   ##
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  Coverage   86.77%   86.77%           
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  Files         311      311           
  Lines       67995    68025   +30     
  Branches    19745    19758   +13     
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+ Hits        59003    59030   +27     
- Misses       4871     4873    +2     
- Partials     4121     4122    +1     

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interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...tions/Simplification/Patterns/Patterns.Rational.cs	99.10% <100.00%> (+0.32%)	⬆️

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[Rafael-SOWNet]

The squash commit, 5d973db, has the right subject, but its body is #2305's message, not this PR's. I took the body from the branch's latest commit that wasn't a merge, and after merging master in, that commit was #2305's squash. This is the message meant for it:

A factor a numerator's terms hold to a power cancels

PairwiseGroupedQuotient pairs a quotient's factors off, and a sum is
one factor to it, so a factor of the denominator inside every term of
the numerator was met only after a rule had taken it out of the sum.
The rules take k out of k*p + k*q and k + k*q, not out of k*p + k^n, so
(x (y + 1) + (y + 1)^2) / (y + 1)^4 was left as written while
(x (y + 1) + (y + 1)) / (y + 1)^2 cancelled to (x + 1) / (y + 1).

Before pairing, a sum on either side now has a polynomial factor of
the other side taken out of it where every term holds that factor, as
it is or to a whole power, the lowest power of it that every term
holds. The pairing then meets it as it meets a factor written out: the
first is (x + y + 1) / (y + 1)^3. A power of a sine is left to the
cancellation it has through the opened angles and a common
denominator: taken out first, it left the second expression of #557
short of 0, at a form one more Simplify takes there.

The quotient rule squares the denominator at each derivative, and the
numerator it writes holds a factor of it, so the derivatives of
e^x / (1 + x^2), simplified at each step, went 21, 149, 629 and 5,117
nodes at the first, third, fifth and seventh; they go 21, 69, 109 and
149. A Taylor expansion to 9 terms took 8 s and takes 1 s, with the
same coefficients.

AFactorHeldToAPowerCancelsTest takes the issue's rows by value as well
as by what they print, and the seventh derivative's size. The suite,
the trio, F#, AOT and the eight harnesses pass.

Fixes #2301.

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