# Questions tagged [simplifying-expressions]

Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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### solving an equation by suggested method [closed]

I have an equation I want to do this issue: T(dV/dT)-V=0 and obtain T that satisfy this relation. How can I do it? we should at first obtain V and then Drivate it. How can?
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### Symbolic properties of Re and Im

I want to define a function f such that f[x] is real whenever x is real. So I define ...
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### Simplifying this expression with Gamma

The Gamma function has the property that $\Gamma(z+1)=\Gamma(z)z$, so this expression: ...
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### How to get the result in terms of a previously defined expression?

Say I have a vector X[n_] := Table[Subscript[x, i], {i, 1, n}] and a matrix of connections: ...
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### How does Simplify deal with contradictions in the assumptions?

Context Sometimes Simplify does generate a warning when the assumptions are self-contradictory. Take this example: ...
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### Eliminate radicals from a symbolic expression

I get a lot of expressions of the type -(((11 + z) (13 - z + Sqrt[25 - 26 z + z^2]))/( 6 (-11 - z + Sqrt[25 - 26 z + z^2]) (7 - z + Sqrt[25 - 26 z + z^2]))) Which ...
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### Why doesn't Mathematica ComplexExpand integrals?

Consider this code example: ComplexExpand[Re[Integrate[f[t], {t, a, b}]]] Mathematica gives me the result as ...
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### Why are these expressions with shifted delta functions not equal?

I have the following equation Exp[a-t]*DiracDelta[t-a] == DiracDelta[t-a] which cannot be evaluated. However, if I plug in 0 for a: ...
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### Why doesn't Mathematica cancel this constant out of the integral?

I have the mathematical expression Integrate[f[r], {r, τ, t}] == a*Integrate[f[r]/a, {r, τ, t}] which is obviously true for all functions ...
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### What did FullSimplify do to deliver a likely wrong expression?

I recently hit a bug in my code and it eventually turns to be a likely error in the simplification of a formula given by FullSimplify. The code is attached and ...
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### Fraction not simplifying — potential precision error [closed]

I have the following fraction which in principle can be simplified such that the term (constant + $\omega$) cancels on the top and bottom. Mathematica is not doing so and I'm guessing it's an issue ...
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### Trouble verifying a solution to a differential equation

I am reading a physics book which has discussed one approach towards solving the differential equation $$\frac{d^2 x(t)}{dt^2} = Cx(t)$$ as follows: Using Mathematica to solve the equation. I tried ...
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### Comparing two equivalent definite integrals

Reading this question on Math.SE, I tried the following Mathematica instructions ...
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### Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?

I am playing around with Simplify amd assumptions. I noticed that: Simplify[x > (a + b)/e, x < (a + b)/e] ...
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### Why is Mathematica telling me that two equal sequences are unequal?

These two sequences are identical: ...
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### How to read Z == 0. - 0.00162663 W

I am solving a set of three linear equations with four variables and found out the values of X, Y and ...
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### Interpreting an expression

When reducing and simplifying a complex algebraic inequality I get an expression containing Root[-a + b #1^3 &, 1] < β < (a/b) How can I interpret the ...
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### Factor independent term from a summation?

Can I factor $t^2$ from $\frac{1}{t}\sum_{n=1}^{n1}t^2Exp[-a n^2+bn]$ to get $t\sum_{n=1}^{n1}Exp[-a n^2+bn]$ using some command? ...
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### Removal of radicals to form algebraic expression

FullSimplify[( Sqrt[(x + h)^2 + y^2] - a) - e (Sqrt[(x - h)^2 + y^2] - b) == 0] How to remove the radicals to obtain an algebraic expression of fourth order using ...
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### Finding the domain in which a function is analytic with no imaginary part

I was wondering if it is easy to see if a given expression evaluates to a real number in a given domain? Let e.g. f(x,y,z) be some function depending on three ...
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### How to solve these complex equations for plot?

I am trying to Plot this code but it is not showing any plot. I want a bistable type plot between "NL" and "P0" and there are six equations and six unknowns. The code is given ...
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### Issues arising when using UnitSimplify for getting a dimensionless expression

I am having some difficulties when using UnitSimplify in manipulating expressions for obtaining dimensionless quantities in Mathematica 12.0.0. Here is a minimal ...
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### Simplify complex expressions

How can I simplify this expression? I tried the functions simplify and FullSimplify. Also the expand function didn't help me. I would like to know about solving such problems in more detail ...
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### Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
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### Better way for constant expressions in functions than storing as global variables?

For example, I wrote a function like this: inversions[list_] := Complement[ Subsets[{1, 2, 3, 8, 4, 7, 6, 5}, {2}], Subsets[list, {2}] ] But as you see, ...
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### Verification of a general solution to d'Alembert equation

I solved a nonlinear differential equation (d'Alembert one) by hand. Mathematica gives the same answer. But I am not able to get Mathematica to verify the solution due to branch cuts. Any one knows of ...
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### Simplify Vs FullSimplify

I performed an integral and received an extremely long answer. I tried running FullSimplify on the answer, and after 72 hours gave up. Does ...
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### When does Solve return root objects and when does it not for cubic equations?

Cubic polynomials always have explicit solutions and Mathematica certainly knows about them. But Mathematica will by default show the explicit solution only sometimes. I'm guessing there is something ...
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### Symplifying expressions with exponentials inside square root

I have an expression $$\exp (i k x) \sqrt{y^2 \exp (-2 i k x)}$$ When I put this in Mathematica and do FullSimplift, it gives ...
I have an expression of this type: $$\left( 1+\frac{a+b}{c}\right)^{d}$$ My question is, how can I collect variables inside parentheses? Of course without putting commands inside parentheses.