Matematika kelas 10 SMA. mohon bantuannya

Matematika kelas 10 SMA. mohon bantuannya

Jawaban Terkonfirmasi

$displaystyle frac{1}{1+sqrt3-sqrt2}=frac{1}{1+(sqrt3-sqrt2)}\frac{1}{1+sqrt3-sqrt2}=frac{1}{1+(sqrt3-sqrt2)}timesfrac{1-(sqrt3-sqrt2)}{1-(sqrt3-sqrt2)}\frac{1}{1+sqrt3-sqrt2}=frac{1-(sqrt3-sqrt2)}{1^2-(sqrt3-sqrt2)^2}\frac{1}{1+sqrt3-sqrt2}=frac{1-sqrt3+sqrt2}{1-5+2sqrt6}\frac{1}{1+sqrt3-sqrt2}=frac12timesfrac{1-sqrt3+sqrt2}{sqrt6-2}timesfrac{sqrt6+2}{sqrt6+2}$
$displaystyle frac{1}{1+sqrt3-sqrt2}=frac12timesfrac{(1-sqrt3+sqrt2)(sqrt6+2)}{(sqrt6)^2-2^2}\frac{1}{1+sqrt3-sqrt2}=frac12timesfrac{sqrt6+2-3sqrt2-2sqrt3+2sqrt3+2sqrt2}{6-4}\frac{1}{1+sqrt3-sqrt2}=frac12timesfrac{2+sqrt6-sqrt2}{2}\boxed{boxed{frac{1}{1+sqrt3-sqrt2}=frac{2+sqrt6-sqrt2}{4}}}$