Question

simplify by taking the lcm... ans it correctly and ill mark u as brilliant ​

Answer 1

Step-by-step explanation:

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

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

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

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

$= \frac{42}{11}$