Mathematica won't simplify the expression with obvious common factor of a fraction - Mathematica Stack Exchange most recent 30 from mathematica.stackexchange.com 2019-10-17T04:46:51Z https://mathematica.stackexchange.com/feeds/question/44609 https://creativecommons.org/licenses/by-sa/4.0/rdf https://mathematica.stackexchange.com/q/44609 4 Mathematica won't simplify the expression with obvious common factor of a fraction an offer can't refuse https://mathematica.stackexchange.com/users/7414 2014-03-24T08:41:51Z 2014-03-24T09:04:22Z <p>I have an expression obtain from an integral, which is:</p> <pre><code>Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify </code></pre> <p>The denominator and numerator of the result have an obvious common factor: </p> <pre><code>Sqrt[Δ^2 + (u - ϵ)^2] </code></pre> <p>How can I let mathematica to cancel this common factor? I have tried <code>Cancel</code> and <code>Refine</code> all the variables to be positive. </p> https://mathematica.stackexchange.com/questions/44609/-/44610#44610 6 Answer by MMM for Mathematica won't simplify the expression with obvious common factor of a fraction MMM https://mathematica.stackexchange.com/users/11001 2014-03-24T09:03:19Z 2014-03-24T09:03:19Z <pre><code>Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // Apart // FullSimplify </code></pre> https://mathematica.stackexchange.com/questions/44609/-/44611#44611 3 Answer by halirutan for Mathematica won't simplify the expression with obvious common factor of a fraction halirutan https://mathematica.stackexchange.com/users/187 2014-03-24T09:04:22Z 2014-03-24T09:04:22Z <p>You could help <em>Mathematica</em> by temporarily renaming the factor.</p> <pre><code>exp = Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify exp /. (Δ^2 + (u - ϵ)^2) :&gt; w FullSimplify[%] /. w :&gt; Δ^2 + (u - ϵ)^2 </code></pre> <blockquote> <p><img src="https://i.stack.imgur.com/Oxz7Y.png" alt="Mathematica graphics"></p> </blockquote>