Cfrgtkky

I do not know how this concept is called in mathematics, but when you are working on an expression, you may operate step by step, saying: "this equals this, and equals this, and equals this..."

But sometimes, you need to specify "this equals this, only if x is not zero", for example when operating and putting x into a denominator.

When drawing on a paper you just write around the equal symbol a note and say: "from now on, x cannot be zero", but I don't know how to express this on a TeX version of a mathematical process representation.

I tried it like this, but it doesn't seem very accurate to me:

What is your suggestion or the standard way of achieving this, if any? Thank you.

Edit:

This is the LaTeX code of the attached image example.

begin{aligned}Lleft[ fleft( tright) right] =int ^{infty }_{0}e^{-st}cdot fleft( tright) dt=lim _{brightarrow infty }int ^{b}_{0}e^{-st}.fleft( tright) dt=lim _{brightarrow infty }left[ int ^{3}_{0}e^{-st}cdot 0cdot dt+int ^{b}_{3}e^{-st}cdot 1cdot dtright] =\

=lim _{brightarrow infty }left[ 0+int ^{b}_{3}e^{-st}cdot 1cdot dtright] =lim _{brightarrow infty }left[ dfrac {e^{-st}}{-s}right] ^{b}_{3}=left[ forall sneq 0right] =end{aligned}

Conditionals in mathematics are often expressed using a { <expr> | <cond> } format, read as <expr> given <cond>. Perhaps consider that here:

documentclass{article}



usepackage{mathtools}

newcommand{Laplace}{mathcal{L}laplace}

DeclarePairedDelimiter{laplace}{[}{]}

newcommand{dt}{,mathrm{d}t}



begin{document}



begin{align*}

  Laplace[big]{f(t)} 

    &= int_0^infty e^{-st} cdot f(t) dt \

    &= lim_{b rightarrow infty} int_0^b e^{-st} cdot f(t) dt \

    &= lim_{b rightarrow infty} biggl[ int_0^3 e^{-st} cdot 0 dt + int_3^b e^{-st} cdot 1 dt biggr] \

    &= lim_{b rightarrow infty} biggl[ 0 + int_3^b e^{-st} cdot 1 dt biggr] \

    &= lim_{b rightarrow infty} biggl[ dfrac {e^{-st}}{-s} biggmvert s neq 0 biggr]_3^b

end{align*}



end{document}

or just include it as a description:

begin{align*}

  % ...

    &= lim_{b rightarrow infty} biggl[ dfrac {e^{-st}}{-s} biggr]_3^b qquad text{(where $s neq 0$)}

end{align*}