Question

Could someone please explain to me how they got this answer?
(√2/2)/(1+√2/2) = √2/(2+√2)

Answer 1

First, let's try to write the left side of the formula in the proper way:

\(\dfrac{\dfrac{\sqrt{2}}{2}}{1+\dfrac{\sqrt{2}}{2}}\), or is it: \(\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{1+\sqrt{2}}{2}}\)?

Answer 2

The first one is correct.

Answer 3

\(\bf \cfrac{
\frac{\sqrt{2}}{2}
}{
1+\frac{\sqrt{2}}{2}
}\qquad recall \implies \cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}\qquad thus
\\ \quad \\
\cfrac{
\frac{\sqrt{2}}{2}
}{
1+\frac{\sqrt{2}}{2}
}\implies \cfrac{
\frac{\sqrt{2}}{2}
}{
\frac{2+\sqrt{2}}{2}
}\implies \cfrac{\sqrt{2}}{2}\cdot \cfrac{2}{2+\sqrt{2}}\implies \cfrac{\cancel{2}\sqrt{2}}{\cancel{2}[2+\sqrt{2}]}\)

Answer 4

OK, the double fractions are ugly, so we will try to get rid of them.
Why not multiply numerator and denominator with 2?

Answer 5

Wait, I see that my good friend @jdoe0001 has done all the work for me (and you).
:(
Wouldn't it be better to leave something to do for @September1620?

Answer 6

I will actually have to write it all out following his work to understand it. If I just wanted the answer to my homework it's already been graded, I'm just trying to understand where I went wrong. Thanks.

Answer 7

YW!