Question 622825
{{{4x/(x+1)+x=(-6)/(x+1)}}}
multiply both sides by (x+1), clear the denominators, results:
4x + x(x+1) = -6
4x + x^2 + x = -6
Arrange as a quadratic equation
x^2 + 5x + 6 = 0
Factors to
(x+3)(x+2) = 0
two solutions
x = -3
and x = -2
;
:
Check solution of x=-3 in the original problem
{{{4(-3)/(-3+1)-3=(-6)/(-3+1)}}}
{{{(-12)/(-2)-3=(-6)/(-2)}}}
+6 - 3 = +3; confirms our solution of x=-3
:
You can can check the x=-2 solution yourself