Given selection of 2 and drag before 5:
We see what we shall obtain if the mouse button is released here.
If the button is released, we obtain the explanation and the result:

Division of both sides by 
is dragged over :
The first is dragged in the parenthesis:
is dragged a bit on the left:
is dragged over which provides :
is dragged over which provides either: or
The choice is presented in a popup menu.
Given a Ctrl+Clic is applied on the selection, giving
Given a Ctrl+Clic is applied on the selection, giving This is a multiplication of like factors.
Given a Ctrl+Clic is applied on , giving
Given a Ctrl+Clic is applied on , giving . This is an addition of like terms.
All the dynamic algebra actions have a mathematical explanation, some have in addition a gesture description.
Given , is dragged before . If the "Describe the dynamic algebra gesture" setting is on, one gets:

Gesture: Multiplicative move of a negative expression to the other side, the factor becomes divisor, the inequality sign is reversed Explanation: division of both sides by 
This is the name of Dynamic Algebra when there limitations to basic gestures and indications of some refused gestures.
When the setting Pedagogical Dynamic Algebra is active, given if one tries to dropt before the fraction, the action is refused with the message: No basic additive output of the numerator.
When the setting is inactive, the action is accepted with the result: and the explanation: Transforming into a sum of 2 fractions or with 2 been factored out.
The idea is that there is no simple action allowing to bring out of the numerator and obtaining an equivalent expression, but that there are two complex actions.
Make some of your calculations on an interactive whiteboard with epsilonwriter, have sometimes students doing so.
Use Dynamic Algebra to write solved exercises. You can delete lines, delete some explanations, and modify others. You will soon have the possibility of modifying the texts used by epsilonwriter for the explanations and descriptions.
Dynamic Algebra is also a more flexible way for typing and modifying formulas. To be used to write documents with formulas.
Use Dynamic Algebra:
To learn the correct gestures with their explanations and their descriptions,
To learn erroneous gestures, learn what we cannot do,
To understand that we cannot make a gesture if we do not know it is correct or not,
To understand that certain gestures are complex and that if we make them in a rough way, we make errors. In algebra, it is necessary to be very precise.
Use the dynamic algebra to make your calculations more easily. It is you who decide on what you want to do, it is the computer which makes it.
Draft your exercises with epsilonwriter, customize your work.
Dynamic Algebra: is included in epsilonwriter, software allowing several persons working on a document. Using Skype in addition, it is ideal for distance tutoring and collaborative work.
The Aristod company, which developed these tools, ceased its activities in April 2019, due to the very low interest that these tools have generated.
JeanFrancois Nicaud, the main author of these tools, keeps them available to users on this website for a few years.
Contact: jeanfrancois dot nicaud at laposte dot net