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Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }

Rationalize the denominator and simplify the expression below Show all steps and calculations to earn full credit You may want to do this work by hand and uploa class=

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The Solution:

The given expression is

[tex]\frac{8}{1-\sqrt[]{17}}[/tex]

Rationalizing the expression with the conjugate of the denominator, we have

[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]

This becomes

[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]

Thus, the correct answer is

[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]

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