What is the value of $frac{(0.5)^{3}-(0.1)^{3}}{(0.5)^{2}+0.5 imes 0.1+(0.1)^{2}} ?$

Let, 0.5 = a, 0.1 = b

$herefore$ Expression $=frac{a^{3}-b^{3}}{a^{2}+a b+b^{2}}$

$=frac{(a-b)left(a^{2}+a b+b^{2} ight)}{a^{2}+a b+b^{2}}=a-b=0.5-0.1=0.4$