Simplify by rationalising the denominator

1.	Simplify by rationalising the denominator
Answer» Step-by-step EXPLANATION: $\frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} } \times \frac{4 - \sqrt{5} }{4 - \sqrt{5} }$ $\frac{ ({4 + \sqrt{5} )}^{2} }{ {4}^{2} - { \sqrt{5} }^{2} } + \frac{ ({4 - \sqrt{5} )}^{2} }{ {4}^{2} - { \sqrt{5} }^{2} }$ $use \: the \: identity \: {a}^{2} + {b}^{2} + 2ab$ $\frac{ {4}^{2} + { \sqrt{5} }^{2} + 2(4 \times \sqrt{5} )}{8 - 5} + \frac{ {4}^{2} + { \sqrt{5} }^{2} - 2(4 \times \sqrt{5} }{8 - 5}$ $\frac{8 + 5 + 8 \times 2 \sqrt{5} }{3} + \frac{8 + 5 - 8 \times 2 \sqrt{5} }{3}$ $\frac{8 + 5 + 8 \times 2 \sqrt{5 } + 8 + 5 - 8 \times 2 \sqrt{5} }{3}$

Answer»

Step-by-step EXPLANATION:

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