How to solve (x-1)/(x+5) > 2

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (x-1)/(x+5) > 2 | Equatix

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Question

$$\frac{ x-1 }{ x+5 } > 2$$

Solve for x

$x\in \left(-11,-5\right)$

Solution Steps

Denominator $x+5$ cannot be zero since division by zero is not defined. There are two cases.

$$x+5>0$$ $$x+5<0$$

Consider the case when $x+5$ is positive. Move $5$ to the right hand side.

$$x>-5$$

The initial inequality does not change the direction when multiplied by $x+5$ for $x+5>0$.

$$x-1>2\left(x+5\right)$$

Multiply out the right hand side.

$$x-1>2x+10$$

Move the terms containing $x$ to the left hand side and all other terms to the right hand side.

$$x-2x>1+10$$

Combine like terms.

$$-x>11$$

Divide both sides by $-1$. Since $-1$ is negative, the inequality direction is changed.

$$x<-11$$

Consider condition $x>-5$ specified above.

$$x\in \emptyset$$

Now consider the case when $x+5$ is negative. Move $5$ to the right hand side.

$$x<-5$$

The initial inequality changes the direction when multiplied by $x+5$ for $x+5<0$.

$$x-1<2\left(x+5\right)$$

Multiply out the right hand side.

$$x-1<2x+10$$

Move the terms containing $x$ to the left hand side and all other terms to the right hand side.

$$x-2x<1+10$$

Combine like terms.

$$-x<11$$