Question

Complete the algebra to show that
1−x^−1−(x−1)(x^−2) simplifies to (1−1/x)^2

Answer 1

\[(1-x^{-1}) - (x-1)(x^{-2})\]Is this your question?

Answer 2

yes

Answer 3

Do you know:\[a^{-1} = \frac{ 1 }{ a }\]Its a index rule.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

@ihatemath33 Got it?

Answer 9

yes thank you!!

Answer 10

you are welcomed!