Solve (x + 4)/(x - 1) > 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for x

$x\in \left(-\infty,-4\right)\cup \left(1,\infty\right)$

Solution Steps

For the quotient to be positive, $x+4$ and $x-1$ have to be both negative or both positive. Consider the case when $x+4$ and $x-1$ are both negative.

$$x+4<0$$ $$x-1<0$$

The solution satisfying both inequalities is $x<-4$.

$$x<-4$$

Consider the case when $x+4$ and $x-1$ are both positive.

$$x-1>0$$ $$x+4>0$$

The solution satisfying both inequalities is $x>1$.

$$x>1$$

The final solution is the union of the obtained solutions.

$$x<-4\text{; }x>1$$