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How do I solve this? I’ve tried every possible way so far yet I get the wrong answer

x>2

Quoted from TWEEKARN\

whats the point

what do you think…

(x/(x-2)) – 1 > 0
x(x-2) – 1 (x-2)^2 > 0
x^2 – 2x – (x^2 -4x + 4) > 0
x^2 – 2x – x^2 + 4x – 4 > 0
2x – 4 > 0
x > 2

if you multiply the whole line it has to be with a positive number so that the inequality does not change sign, so you use the square of the denominator (x-2).

Quoted from atmo

(x/(x-2)) – 1 > 0
x(x-2) – 1 (x-2)^2 > 0
x^2 – 2x – (x^2 -4x + 4) > 0
x^2 – 2x – x^2 + 4x – 4 > 0
2x – 4 > 0
x > 2

thanks, why can’t I multiple by x-2 at the beginning though

Quoted from Bonkers

if a/b > 0 then a*b > 0

so (a/b > 0) = (a*b > 0)?

Why can’t I then?
(X/(X-2))-1 > 0
x^2-2x-1 > 0

that gives wrong answer :I

Quoted from jx53

Quoted from atmo

(x/(x-2)) – 1 > 0
x(x-2) – 1 (x-2)^2 > 0
x^2 – 2x – (x^2 -4x + 4) > 0
x^2 – 2x – x^2 + 4x – 4 > 0
2x – 4 > 0
x > 2

thanks, why can’t I multiple by x-2 at the beginning though

Because you don’t know what value x-2 has at this point. If x turned out to be 0.5, then x-2 would be a negative number so you would be multiplying your inequality be a negative which means you have to change the inequality sign from > to <. That's why you square it to ensure that you are multiplying by a positive.

Quoted from jx53

[…]

what do you think…

that youll never have use for this at all