Solve the inequality:

1. x^2 - (2/x) > 0

2. (x-5)^4 / (x(x+3)) ≥ 0

Thank you for any help!

2. Originally Posted by live_laugh_luv27

Solve the inequality:

1. x^2 - (2/x) > 0
$x^{2}-\frac{2}{x}=\frac{x^{3}-2}{x}=\frac{\left( x-\sqrt[3]{2} \right)\left( x^{2}+\sqrt[3]{2}x+\sqrt[3]{4} \right)}{x}>0,$ and since $x^{2}+\sqrt[3]{2}x+\sqrt[3]{4}>0,$ you just need to solve $\frac{x-\sqrt[3]{2}}{x}>0.$

Originally Posted by live_laugh_luv27

2. (x-5)^4 / (x(x+3)) ≥ 0
Numerator is always positive (and zero when $x=5$), so, you just need to solve $x(x+3)>0.$

3. Thanks for your help, I really appreciate it!