How does
(3√2)/6 - (8√2)/216 = (100√2)/216 ?
Thanks
The LCD of 6 and 216 is 216.
Multiply the first term by 36/36
$\displaystyle \frac{36}{36} \cdot \frac{3\sqrt{2}}{6} = \frac{108 \sqrt2}{216}$
Now they have the same denominator they can be combined
$\displaystyle \frac{108 \sqrt{2} - 8 \sqrt{2}}{216}$
Factor out $\displaystyle \sqrt{2}$
$\displaystyle \frac{\sqrt{2}(108-8)}{216} = \frac{100\sqrt2}{216}$
This equals the RHS but since both numerator and denominator are multiples of 4 we can cancel it down to $\displaystyle \frac{25 \sqrt{2}}{54}$