Question

simplify the following by rationalising the denominator 4+root5/4_root5 + 4_root 5 / 4+root
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Answer 1

Answer:

$\frac{42}{11}$

Step-by-step explanation:

$\frac{4+\sqrt{5}}{4-\sqrt{5}} + \frac{4-\sqrt{5}}{4+\sqrt{5}}$

= $\frac{(4+\sqrt{5})^2 +(4-\sqrt{5})^2}{(4-\sqrt{5})(4+\sqrt{5})}$

= $\frac{(16+8\sqrt{5}+5) + (16-8\sqrt{5}+5) }{(16 - 5)}$                                    

= $\frac{(21 + 21)}{(11)}$

= $\frac{42}{11}$