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The phrase "which shows how" is correct and usable in written English.
You can use it to introduce an explanation of a process or to provide an example that explains something. For example, "She prepared a delicious dish which shows how creative she can be in the kitchen."
Exact(60)
Which shows how much things have changed.
Which shows how clueless I was, even then.
Which shows how ordinary people do extraordinary things.
"Which shows how useful that advice can be," Mr. St.
Most universities have a "Course Equivalency Guide", which shows how your courses transfer to their school.
"There is a large body of public health research which shows how food insecurity affects health".
She legitimately had a chance to make the cut, which shows how good she played.
We end up laughing, helplessly, which shows how much football has to change.
Before the start I thought they would win, which shows how much I know.
Here's their session on BBC Introducing, which shows how good they are.
(I thought that last was a joke, which shows how much I know).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com