Question

The value of $\frac{(119{)}^2+(119\left)\right(111)+(111{)}^2}{(119{)}^3-(111{)}^3}$ is:

• A. $8$
• B. $\frac{1}{8}$
• C. $230$
• D. $\frac{1}{230}$

Answer 1

The correct option is B $\frac{1}{8}$

$\frac{(119{)}^2+(119\left)\right(111)+(111{)}^2}{(119{)}^3-(111{)}^3}$

Let $a=119$ and $b=111$

From, $a^3-b^3=(a-b)(a^2+ab+b^2)$

$=\frac{(119{)}^2+(119\left)\right(111)+(111{)}^2}{(119-111)\left(\right(119{)}^2+\left(119\right)\left(111\right)+\left(111{)}^2\right)}$

$=\frac{1}{8}$