Question

Root5 /2 root5 -1

Answer 1

Answer:

10, 5, 19

Step-by-step explanation:

Recall that

${a}^{2} - {b}^{2} = (a + b)(a - b)$

So we can multiply the fraction by

$\frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 }$

And get

$\frac{ \sqrt{5} }{2 \sqrt{5} - 1} \times \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } = \frac{10 + \sqrt{5} }{20 - 1} = \frac{10 + \sqrt{5} }{19}$