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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​

Respuesta :

Alfpfeu

Answer:

Step-by-step explanation:

Hello,

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

[tex]\dfrac{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[/tex]

So the solution is

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

Thanks

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