Question

((x+1/x^2)^2)/((x+1/x^2)-1) what is the simplified from of this not foiled

Answer 1

the simplest form i can get it to is ((x+1)^2)/(x^2(x+1)-x^4). can it be simplified further?

Answer 2

Original form:
\[\frac{ (\frac{ x+1 }{ x ^{2} })^{2} }{ \frac{ x+1 }{ x^{2} }-1 }\]

Simplified:
\[\frac{ \frac{ (x+1)^{2} }{ x ^{4} } }{ \frac{ x+1-x^{2} }{ x^{2} } }\]

\[ \frac{ (x+1)^{2} }{ x ^{4} } . \frac{ x^{2} } { x+1-x^{2} }\]

\[ \frac{ (x+1)^{2} }{ x ^{2}(x+1-x^{2}) } \]

\[ \frac{ x^{2}+2x+1 }{ x ^{3}+x^2-x^{4}} \]

Answer 3

Thank you