How to rewrite x/ (x-2) > 2 in the form P(x)/ Q(x) > 0?

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To rewrite the inequality x/(x-2) > 2 in the form P(x)/Q(x) > 0, first clarify the expression by ensuring proper parentheses. Begin by subtracting 2 from both sides to combine terms. This leads to the inequality x/(x-2) - 2 > 0. Next, express the left side as a single rational expression, resulting in (x - 2(x-2))/(x-2) > 0. This simplifies to (x - 2x + 4)/(x-2) > 0, or (-x + 4)/(x-2) > 0.
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Solve x/ x-2 >2 by first rewriting it in the form P(x) / Q(x) >0


How do I go about first rewriting it into that form?
 
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elmosworld403 said:
Solve x/ x-2 >2 by first rewriting it in the form P(x) / Q(x) >0

How do I go about first rewriting it into that form?
I assume you mean , Solve x/(x-2) > 2 .

Parentheses are important. What you wrote literally means \displaystyle \ \ \frac{x}{x}-2>2\ .To get started on the problem, add 2 to both sides.

Then make the expression on the left side into one rational expression.
 
SammyS said:
I assume you mean , Solve x/(x-2) > 2 .

Parentheses are important. What you wrote literally means \displaystyle \ \ \frac{x}{x}-2>2\ .

Yes sorry

X/ (X-2) > 2


and form (P(x))/(Q(x)) > 0
 
Last edited:
elmosworld403 said:
Yes sorry

X/ (X-2) > 2

and form (P(x))/(Q(x)) > 0
See the little bit I added to my previous post after you quoted it.
 

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