Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify $\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$

Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify
$\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$

Answers

(3 -$\sqrt7)(3 + \sqrt7$)

= 9 + 3$\sqrt7 \; -3\sqrt7 \; -\sqrt49$

= 9 + 3$\sqrt7\; -3\sqrt7\; - 7 = 2$

= $\frac{2(3\; +\sqrt7)\; 2(3\; -\sqrt7)}{2}$

= $\frac{(6\; + 2\sqrt7)\; -(6 + 2\sqrt7)}{2}$ = $\frac{4\sqrt7}{2}$

Simplifies to 2$\sqrt7$

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johnmulu answered the question on March 7, 2017 at 14:10

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