SOLUTION: Solve the equation by introducing a substituition that transforms this equation to quadratic form. 3=1/(x+1)^2+2/(x+1)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the equation by introducing a substituition that transforms this equation to quadratic form. 3=1/(x+1)^2+2/(x+1)       Log On


   

Question 210919: Solve the equation by introducing a substituition that transforms this equation to quadratic form.
3=1/(x+1)^2+2/(x+1)
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
3=1/(x+1)^2+2/(x+1)
.
Let t = 1/(x+1)
then, substitute the above in to the original:
3 = t^2 + 2t
0 = t^2 + 2t - 3
0 = (t+3)(t-1)
t = {-3,1}
.
But, remember t = 1/(x+1)
-3 = 1/(x+1)
-3(x+1) = 1
-3x-3 = 1
-3x = 4
x = -4/3
.
1 = 1/(x+1)
(x+1) = 1
x = 0
.
x = {-4/3, 0}