Another way....you are dividing by a fraction, so flip the denominator and multiply
(1 + sqrt(2)) x 2/sqrt (2)= 2/ sqrt2 +1
Then simplify the first term by multiplying by sqrt2/sqrt2
sqrt2/sqrt2 (2/sqrt2) + 1 = 1 + sqrt2
This isn't as bad as it looks
[ 1 + √2 / 2 ] / [√2 / 2] get a common denominator on top
[ (2 + √2 ) / 2 ] / [√2 / 2] the "2's" in each denominator "cancel"
[2 + √2 ] / √2 =
2/√2 + √2 / √2 =
[√2 * √2 ] / √2 + √2 / √2
√2 + 1
And that's it !!!
Another way....you are dividing by a fraction, so flip the denominator and multiply
(1 + sqrt(2)) x 2/sqrt (2)= 2/ sqrt2 +1
Then simplify the first term by multiplying by sqrt2/sqrt2
sqrt2/sqrt2 (2/sqrt2) + 1 = 1 + sqrt2