Question

Simplify by rationalizing the denominator 4 + root5 / 7 root5 + 4 root5 / 4 + root5

Answer 1

$\frac{4+\sqrt5}{7 \sqrt5}+\frac{4 \sqrt5}{4+\sqrt5}=\frac{(4+\sqrt5)(\sqrt5)}{7 \sqrt5*\sqrt5}+\frac{4 \sqrt5*(4-\sqrt5}{(4+\sqrt5)(4-\sqrt5)}\\\\=\frac{5+4\sqrt5}{35}+\frac{-20 +16\sqrt5}{11}=\frac{-645+604 \sqrt5}{385}$

Answer 2

4 + √5 / 7√5 + 4 √5 /4 + √5

= ( 4 + √5 ) ( √5 )/ 7√5 × √5 + 4√5 × ( 4 - √5)/(4+√5)(4-√5)

= (5 + 4√5 )/ 35 + (-20 + 16√5)/11

= - 645 + 604√5 / 385