Question

How do I simplify, \[\frac{ {x}^{-1/2}({2x}^{1/2}- {x}^{-1/2}) }{ x^{-1} }\]

Answer 1

\(\Large {\bf a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\\ \quad \\ \quad \\
\cfrac{
x^{-\frac{1}{2}}\left(2x^{\frac{1}{2}}-x^{-\frac{1}{2}}\right)
}{
x^{-1}
}\implies \cfrac{

\frac{1}{\square ?}\left(2x^{\frac{1}{2}}-\frac{1}{\square ?}\right)}{\frac{1}{\square ?}}}\)

just like before, distribute and combine exponents

Answer 2

@jdoe0001 this isn't making any sense to me.

Answer 3

Distribute the numerator, with the additional of exponents
\[= \frac{2x^{(-1/2+1/2)}-x^{(-1/2-1/2)}}{x^{-1}}= \frac{2x^0 - x^{-1}}{x^{-1}}\]
\[=\frac{2-x^{-1}}{x^{-1}} = \frac{2}{x^{-1}} - 1 = 2x-1\]

Answer 4

@linh412986 my textbook has the answer as being x-2

Answer 5

Hello @tiffanykeys, I have no idea. If your problem is correct, then the answer should be wrong :) Anyway, you may check and solve it with distributing and exponent operations.