Question

x-3 over x-5> 0 i really need help asap

Answer 1

x > 3 over x + 5

Answer 2

\[\frac{ x - 3 }{ x - 5 } > 0\]

try multiplying both sides by x - 5, and be careful to adjust the inequality when the denominator is negative.

Answer 3

For this inequality to be false, either \(x-3\) or \(x-5\) (not both) is negative or zero.

We can see that for \(x-3\) to be negative or zero, \(x\le3\)
And for \(x-5\) to be negative or zero, \(x\le5\)

So x need to be in range \([3,5]\), where \(x-3\) is positive or zero, but \(x-5\) is negative or zero.

So multiplying both sides by \(x-5\), you have \[x-3<x-5,~3\le x\le5\]
(NOTE that we flipped the sign because \(x-5\) is negative)
Subtract both sides by \(x\), and you have \(-3 < -5\) which is not true.

So \(x\) cannot be in range \([3,5]\)

So you have \(\boxed{x <3\text{ or }x>5}\)