(2*x-3)/(x+1)>1 inequation

Given the inequality:
$$\frac{2 x - 3}{x + 1} > 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x - 3}{x + 1} = 1$$
Solve:
Given the equation:
$$\frac{2 x - 3}{x + 1} = 1$$
Multiply the equation sides by the denominator 1 + x
we get:
$$2 x - 3 = x + 1$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = x + 4$$
Move the summands with the unknown x
from the right part to the left part:
$$x = 4$$
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$\frac{2 x - 3}{x + 1} > 1$$
$$\frac{-3 + \frac{2 \cdot 39}{10}}{1 + \frac{39}{10}} > 1$$

48    
-- > 1
49    

Then
$$x < 4$$
no execute
the solution of our inequality is:
$$x > 4$$

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