Explanation:
I guess the equation is
(2x + 5)/(x + 4) = 1
then we multiply both sides by (x + 4) and get
2x + 5 = x + 4
x + 5 = 4
x = -1
but if the equation is truly as you wrote it :
2x + 5/x + 4 = 1
then we multiply both sides by x (to eliminate the fraction) :
2x² + 5 + 4x = x
2x² + 3x + 5 = 0
and we need to solve as quadratic equation
ax² + bx + c = 0
x = (-b ±sqrt(b² - 4ac))/(2a)
in our case
a = 2
b = 3
c = 5
we get
x = (-5 ±sqrt(5² - 4×2×5))/(2×2) =
= (-5 ±sqrt(25 - 40))/4 = (-5 ±sqrt(-15))/4
as we see, the solution contains the square root of a negative number (-15). so, this has no real number as solution (only complex/imaginary numbers based on i = sqrt(-1)) :
x1 = (-5 + sqrt(15)i)/4
x2 = (-5 - sqrt(15)i)/4
you see, how important it is to write an expression correctly ?