(100-x^2)^(1/2) / (100-x^2)^(-1/2)

asked by guest
on Nov 14, 2024 at 2:39 pm



You asked:

Evaluate the expression: \(\frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}} = 100 - x^{2} \)

Expanded

\[\frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}} = 100 - x^{2}\]

Factored

\[\frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}} = \sqrt{- \left(x - 10\right) \left(x + 10\right)} \left(- \left(x - 10\right) \left(x + 10\right)\right)^{\frac{1}{2}}\]

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