- #1

Rectifier

Gold Member

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The problem

The problem

$$ \frac{x+4}{x-1} > 0 $$

**The attempt at a solution**

As I can see ##x \neq 1##. I want to muliply both sides of the expression with x-1 to get rid of it, from the fraction. But before that, I have to consider two cases where x-1 is bigger and smaller than 0 because the sign gets inverted when multiplying (or dividing) by a negative number.

Case 1:

## x-1 > 0 \\ x >1 ## gives

$$ \frac{x+4}{x-1} > 0 \\ \\ x+4 > 0 \\ x > -4$$

Case 2:

## x-1 < 0 \\ x < 1 ## gives

$$ \frac{x+4}{x-1} > 0 \\ \\ x+4 < 0 \\ x < -4$$

*This is the place where I get stuck. I am not sure how to take all this information and produce an answer.*