Question

given the function R(x)= x+5/x-5 find the value of x that make the function greater then or equal to zero. write the solution in interval notation​

Answer 1

(−∞,−5]∪(5,∞)

Answer 2

Explanation:

Hello,

First of all, let s take x real number different from 5, as we cannot divide by 0

`(x+5)/(x-5)\geq 0 \\ \\<=> (x+5\geq 0 \ and \ x-5> 0) \ or \ (x+5\leq 0 \ and \ x-5< 0) \\ \\<=> (x\geq -5 \ and \ x> 5) \ or \ (x\leq -5 \ and \ x< 5)\\ \\<=> x> 5 \ or \ x\leq -5`

So the solution is

`\Large \boxed{\sf \bf ]-\infty;-5]\cup]5;+\infty[}`

Thanks