Im not sure how to times through by 3/3 on the bottom
(2/3) / (1+(2/3)^2)^0.5
trying to get 2/(9+4x^2)^0.5 If somebody could show me how that'd be much appreciated
I'm sure you mean the following:
$\displaystyle \frac{ \frac{2}{3} }{ \sqrt{1 + \left( \frac{2x}{3} \right) ^{2}} }$
Observe the $\displaystyle \frac{2}{3}$ in the numerator. We can move that 3 to the denominator of the entire function.
Giving us:
$\displaystyle \frac{ 2 }{ 3 \sqrt{1 + \left( \frac{2x}{3} \right) ^{2}} }$
But we also know that:
$\displaystyle 3 = \sqrt{9}$
Thus:
$\displaystyle \frac{ 2 }{ \sqrt{9} \sqrt{1 + \left( \frac{2x}{3} \right) ^{2}} }$
Simplify the denominator.
$\displaystyle \frac{ 2 }{ \sqrt{9(1 + \left( \frac{2x}{3} \right) ^{2})} }$
$\displaystyle \frac{ 2 }{ \sqrt{9(1 + \left( \frac{4x^2}{9} \right) )} }$
$\displaystyle \frac{ 2 }{ \sqrt{9 + 4x^2 } }$