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(x+3)/(x-11)>0 inequation

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x + 3     
------ > 0
x - 11

\frac{x + 3}{x - 11} > 0

(x + 3)/(x - 11) > 0

Detail solution

Given the inequality:

\frac{x + 3}{x - 11} > 0

To solve this inequality, we must first solve the corresponding equation:

\frac{x + 3}{x - 11} = 0

Solve:
Given the equation:

\frac{x + 3}{x - 11} = 0

Multiply the equation sides by the denominator -11 + x
we get:

x + 3 = 0

Move free summands (without x)
from left part to right part, we given:

x = -3

x_{1} = -3

x_{1} = -3

This roots

x_{1} = -3

is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:

x_{0} < x_{1}

For example, let's take the point

x_{0} = x_{1} - \frac{1}{10}

-3 + - \frac{1}{10}

- \frac{31}{10}

substitute to the expression

\frac{x + 3}{x - 11} > 0

\frac{- \frac{31}{10} + 3}{-11 + - \frac{31}{10}} > 0

1/141 > 0

the solution of our inequality is:

x < -3

 _____          
      \    
-------ο-------
       x1

Solving inequality on a graph

Rapid solution [src]

Or(And(-oo < x, x < -3), And(11 < x, x < oo))

\left(-\infty < x \wedge x < -3\right) \vee \left(11 < x \wedge x < \infty\right)

((-oo < x)∧(x < -3))∨((11 < x)∧(x < oo))

Rapid solution 2 [src]

(-oo, -3) U (11, oo)

x\ in\ \left(-\infty, -3\right) \cup \left(11, \infty\right)

x in Union(Interval.open(-oo, -3), Interval.open(11, oo))