Question

(a-b)/(a^1/2-b^1/2) - (a^3/2-b^3/2)/(a-b)

Answer 1

$frac{a-b}{a^{1/2}-b^{1/2}} - frac{a^{3/2}-b^{3/2}}{a-b} = frac{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}{a^{1/2}-b^{1/2}} - frac{(a^{1/2}-b^{1/2})(a+a^{1/2}b^{1/2}+b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}= \\= frac{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})^2}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})} -frac{(a^{1/2}-b^{1/2})(a+a^{1/2}b^{1/2}+b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})} =\\= frac{(a^{1/2}-b^{1/2})(a+2a^{1/2}b^{1/2}+b-a-a^{1/2}b^{1/2}-b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}=$
=$frac{a^{1/2}b^{1/2}}{a^{1/2}+b^{1/2}}} = frac{ sqrt{a}* sqrt{b} }{ sqrt{a} + sqrt{b} }$

Answer 2

a-b=(a^{1/2})^2 -(b^{1/2})^2 - разность квадратов