Factorization of 1/xyz(x² + y² + z²) + 2(1/x + 1/y + 1/z)
The factorized form of \[ \frac{1}{xyz}(x^2+y^2+z^2)+2\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \] is ___________
Solution
\[ \frac{x^2+y^2+z^2}{xyz} + 2\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \]
\[ = \frac{x^2+y^2+z^2+2xy+2yz+2zx}{xyz} \]
\[ = \frac{(x+y+z)^2}{xyz} \]
\[ \boxed{\frac{(x+y+z)^2}{xyz}} \]