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Here is the code I used in SageMath computations.

var('a11,a12,a21,a22,b1,b2')

A = matrix([[a11,a12,b1],[a21,a22,b2]])

A.add_multiple_of_row(1,0,-a21/a11)

pretty_print(A)

The output is as follows. image description

Is it possible to simplify the entries in the form a/b?

Thanks for your time.