First, take all expressions to one side of the inequality:
[tex]\displaystyle{ 3+\frac{4}{x}- \frac{x+2}{x} \geq 0 [/tex].
Multiply 3 by [tex]\displaystyle{ \frac{x}{x} [/tex] to write it as a fraction with denominator equal to the other expressions
[tex]\displaystyle{ \frac{3x}{x}+\frac{4}{x}- \frac{x+2}{x} \geq 0 [/tex].
Since all three expressions have equal denominator, we collect them into one rational expression as follows:
[tex]\displaystyle{ \frac{3x+4-x-2}{x} [/tex], which is equal to [tex]\displaystyle{ \frac{2x+2}{x} [/tex].
Thus the inequality is [tex]\displaystyle{ \frac{2x+2}{x} \geq 0[/tex].
Answer: A
