Answer to Question #90373 in Algebra for Michael key

Question

1. Solve the following inequlity 2x/x-2>x+4

Answer 1

$\frac{2x}{x-2}>x+4$

If $x>2:\;\;2x>(x-2)(x+4)$ or $x^2<8$ or $2<x<2\sqrt{2}$ .

If $x<2:\;\;2x<(x-2)(x+4)$ or $x^2>8$ or $-\infty<x<-2\sqrt{2}$

Answer: $2<x<2\sqrt{2}\;\;or\;\;-\infty<x<-2\sqrt{2}$