We can factor out x, y and z in the right hand side. This cancels out the denominator of x, y and z when we substitute in the expressions given in the question:
Written by me in LaTeX
Which is what we needed to show.
Next, we need to show that yz + zx + xy = -1. To obtain an expression in x, y, and z, we should use the determinant of the matrix, which we will call A. What is the determinant of A?
We are given that A maps the following vector to the zero vector:
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