Simplify the following and show the solutions completely.
(x/x+4)–(5/x)

The following is the expression in simplified form;

The solutions are;

x = 5/2 + √(105) or 5/2 - √(105)

Explanation:

The given expression is written as follows;

We multiply the denominators to form a common denominator and then multiply each individual fraction numerator by the factor of the common denominator from the other fraction as follows;

The above expression is simplified to get;

To find the solution of the expression, we equate then expression to zero as follows;

Which gives;

x² - 5·x - 20 = 0 × (x² + 4·x) = 0

x² - 5·x - 20 = 0

Solving with the quadratic equation,  where;

a = 1

b = -5

c = -20

We get;

Therefore, the solutions are;

x = 5/2 + √(105) or 5/2 - √(105).