Chapter 0 - Section 0.6 - Solving Miscellaneous Equations - Exercises - Page 34: 16

$x=0, x=\pm \sqrt 2$

$\frac{6x(x^{2}+1)^{2}(x^{2}+2)^{4}-8x(x^{2}+1)^{3}(x^{2}+2)^{3}}{(x^{2}+2)^{8}}=0$ $\frac{2x(x^{2}+1)^{2}(x^{2}+2)^{3}(3(x^{2}+2)-4(x^{2}+1))}{(x^{2}+2)^{8}}=0$ $\frac{2x(x^{2}+1)^{2}(x^{2}+2)^{3}(-x^{2}+2)}{(x^{2}+2)^{8}}=0$ $x=0, x=\pm \sqrt 2$