Question

simplify radical(1-x^2). the answer comes out to be (-x/(radical(1-x^2))) but I dont know the steps to get there???

Answer 1

Congrats

Answer 2

\[\sqrt{1-x^2} \cdot \frac{\sqrt{1-x^2}}{\sqrt{1-x^2}}=\frac{1-x^2}{\sqrt{1-x^2}}\]

Answer 3

Well now you have to rationalize the denominator right?

Answer 4

\[\sqrt{1-x^2} \neq \frac{-x}{\sqrt{1-x^2}}\]

Answer 5

counterexample:
choose x=1/2
\[\sqrt{1-(\frac{1}{2})^2}=\sqrt{1-\frac{1}{4}}=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\]
\[\frac{-\frac{1}{2}}{\sqrt{1-(\frac{1}{2})^2}}=\frac{-1}{2} \cdot \frac{1}{\sqrt{1-(\frac{1}{2})^2}}=\frac{-1}{2} \cdot \frac{1}{\frac{\sqrt{3}}{2}}=\frac{-1}{2} \cdot \frac{2}{\sqrt{3}}=\frac{-1}{\sqrt{3}}\]

Answer 6

\[\frac{\sqrt{3}}{2} \neq \frac{-1}{\sqrt{3}}\]