If A =$$\frac{0.125 + 0.729}{0.25 - 0.45 + 0.81} - 0.25 + \frac{12}{20}-\frac{6}{8}$$​, then the value of A is.

Correct option is A

​Given:

​$$A = \frac{0.125 + 0.729}{0.25 - 0.45 + 0.81} - 0.25 + \frac{12}{20}-\frac{6}{8}$$ 

Concept Used: ​

$$(a+b)^3 = (a+b)(a^2+b^2-ab)$$​​

Solution: ​

​$$A = \frac{0.125 + 0.729}{0.25 - 0.45 + 0.81} - 0.25 + \frac{12}{20}-\frac{6}{8} \\ \ \\A = \frac{(0.5)^3 + (0.9)^3}{(0.5)^2 - 0.5\times 0.9 + (0.9)^2} - 0.25 + 0.6-0.75 \\ \ \\A = \frac{[(0.5) + (0.9)][(0.5)^2 - 0.5\times 0.9 + (0.9)^2]}{(0.5)^2 - 0.5\times 0.9 + (0.9)^2} - 0.4 \\ \ \\A = [(0.5) + (0.9)] - 0.4 \\ \ \\ A = 1.4-0.4 \\ \ \\ A = 1$$​​