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

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

Algebra
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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