When using \[...\] I noticed sometimes the vertical space used is larger than in other cases that also uses \[...\]. I do not understand why this is the case. Here is an example
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
The solution found in (1) now becomes%
\[
f\left( x\right) e^{bx}=F\left( x\right)
\]
Then (1) becomes%
\[
u\left( t,x\right) =e^{-at}e^{bx}f\left( x-ct\right)
\]
QED.
\end{document}
which gives

The first equation uses more space above and below than the second equation.
Question: Is it possible to make \[..\] use smaller vertical space above and below the equation, just like in case B?
Also, when using align, the spaces in both cases now becomes the same.
Question: Can one reduce this vertical space as well to be as in case B above?
Here is MWE for align
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
The solution found in (1) now becomes%
\begin{align*}
f\left( x\right) e^{bx}&=F\left( x\right)
\end{align*}
Then (1) becomes%
\begin{align*}
u\left( t,x\right) =e^{-at}e^{bx}f\left( x-ct\right)
\end{align*}
QED.
\end{document}
Here screen shot side by side showing the difference:

ps. I know about savetrees package, but it had some side effects I did not like so I do not want to use it for this purpose.
Using Tl 2019

\abovedisplayskip, (ii) use onlyamsmathenvironments which not consider\abovedisplayshortskip. See https://tex.stackexchange.com/questions/385774/amsmath-redefine-align-to-support-abovedisplayshortskip-and-belowdisplayshor/386052 – Zarko Sep 06 '19 at 06:16equation(*). – daleif Sep 06 '19 at 09:12