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sqrt(4*x^3+3*x^2-4x-3)/sqrt(9-x^2

 Sep 26, 2020
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\(\frac{\sqrt{4x^3+3x^2-4x-3}}{\sqrt{9-x^2}}\qquad -3 4x^3+3x^2-4x-3=(x+1)(x+0.75)(x-1)\\ \text{This is only }\ge0  \text{  in the regions } [-1,-0.75]\;\;\; and \;\;\;[1,\infty)\\ so\\ \text{This cannot be greatly simplified}\\~\\ \frac{\sqrt{4x^3+3x^2-4x-3}}{\sqrt{9-x^2}}\\=\sqrt{\frac{4x^3+3x^2-4x-3}{9-x^2}} \\~\\ \text{In the real number system the restrictions on x are}\;\;\; [-1,-0.75]\;\;\; and \;\;\;[1,3)\\ \)

 

 

 

 

LaTex:

\frac{\sqrt{4x^3+3x^2-4x-3}}{\sqrt{9-x^2}}\qquad -3

4x^3+3x^2-4x-3=(x+1)(x+0.75)(x-1)\\
\text{This is only }\ge0  \text{  in the regions } [-1,-0.75]\;\;\; and \;\;\;[1,\infty)\\
so\\
\text{This cannot be greatly simplified}\\~\\
\frac{\sqrt{4x^3+3x^2-4x-3}}{\sqrt{9-x^2}}\\=\sqrt{\frac{4x^3+3x^2-4x-3}{9-x^2}} \\~\\
\text{In the real number system the restrictions on x are}\;\;\; [-1,-0.75]\;\;\; and \;\;\;[1,3)\\

 Sep 27, 2020
edited by Melody  Sep 27, 2020

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