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The phrase "approaching that of" is correct and usable in written English.
It can be used when comparing two things, indicating that one is getting closer in quality, quantity, or degree to another.
Example: "The performance of the new model is approaching that of its more expensive competitors."
Alternatives: "nearing that of" or "coming close to".
Exact(60)
Single-stranded DNA parvoviruses have been shown to have a mutation rate approaching that of RNA viruses [44], [45].
Her mood was now approaching that of her dress.
Lipids give cell membranes a fluid character, with a consistency approaching that of a light oil.
Accelerated to speeds approaching that of light, the particles give off electromagnetic radiation by synchrotron emission.
Hamas controls Gaza, which has a Palestinian population approaching that of the West Bank.
Today the country's birthrate -- at 2.1 -- is approaching that of the United States.
But to say that business was approaching that of the boom years would be an overstatement.
Fibres made from carbon nanotubes (CNTs) have not yet achieved strengths approaching that of individual CNTs.
The test results show that both types of joints had excellent strengths, approaching that of the composite sandwich reference specimens.
In many cases these developmental processes, contingencies, and comorbidities involve long causal periods, approaching that of the entire human lifespan.
This allows to obtain higher current levels in finite cells, approaching that of the semi-infinite case.
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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