(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: (100−x2)12(100−x2)−12\frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}}

MathBot Answer:

Evaluated



(100−x2)12(100−x2)−12=100−x2\displaystyle \frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}} = 100 - x^{2}

Expanded

(100−x2)12(100−x2)−12=100−x2\frac{{\left( 100 - {x}^{2} \right)}^{\frac{1}{2}}}{{\left( 100 - {x}^{2} \right)}^{\frac{-1}{2}}} = 100 - x^{2}

Factored

(100−x2)12(100−x2)−12=−(x−10)(x+10)(−(x−10)(x+10))12\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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