Question

x/(x+1)-x^2-1 = (-x^3-x^2+2x+1)/x+1
How do I get that answer (STEPS)

Answer 1

x/(x+1)-(x+1)(x-1)=(-x^3-x^2+2x+1)/x+1

Answer 2

Let's solve your equation step-by-step.
x
x+1
−x2−1=
−x3−x2+2x+1
x
+1
x
x+1
+−x2+−1=
−x3−x2+2x+1
x
+1
Multiply all terms by (x+1)(x) and cancel:
xx+(−x2)(x+1)(x)+−1(x+1)(x)=(−x3−x2+2x+1)(x+1)+1(x+1)(x)
−x4−x3−x=−x4−2x3+2x2+4x+1(Simplify both sides of the equation)
−x4−x3−x−(−x4−2x3+2x2+4x+1)=−x4−2x3+2x2+4x+1−(−x4−2x3+2x2+4x+1)(Subtract -x^4-2x^3+2x^2+4x+1 from both sides)
x3−2x2−5x−1=0
(Use cubic formula)
x=−1.285142,−0.221876,3.507019
Check answers. (Plug them in to make sure they work.)
x=3.507019(Works in original equation)
x=−1.285142(Works in original equation)
x=−0.221876(Works in original equation)
Answer:
x=3.507019 or x=−1.285142 or x=−0.221876

Answer 3

@Dengeki

Answer 4

@ryanwhite499 Thanks