Good evening,

I am learning maths from scratch with some online websites and PDFs, so my level is pretty low.

I am stuck with this simple expression with radical terms:

"Write 4/1 + √5 in simplest form.

Solution
Begin by finding the conjugate of the denominator by writing the denominator and changing the sign.

So the conjugate of 1 +√5 is 1 − √5.

Then multiply the fraction by 1 − √5/1 − √5

4/1 + √5 X 1 − √5/1 − √5 =

4 − 4√5/−4 =

√5 − 1"

What I am missing is the very result. How do you obtain √5 − 1 from 4 − 4√5/−4 = ? Can anybody please explain to me which rule I should apply to get it?

Thank you very much in advance!

Claudia

$\dfrac{4}{1+\sqrt{5}} \cdot \dfrac{1-\sqrt{5}}{1-\sqrt{5}} = \dfrac{4(1-\sqrt{5})}{1-5} = \dfrac{4(1-\sqrt{5})}{-4} = -(1-\sqrt{5}) = \sqrt{5}-1$

$\dfrac{4}{1+\sqrt{5}} \cdot \dfrac{1-\sqrt{5}}{1-\sqrt{5}} = \dfrac{4(1-\sqrt{5})}{1-5} = \dfrac{4(1-\sqrt{5})}{-4} = -(1-\sqrt{5}) = \sqrt{5}-1$