If (a+1)/a = k, what is the value of $$\frac{(a^2-1)}{a^2}$$​?

Correct option is A

Given:

​$$\frac{a+1}{a}=k$$

Formula used:

​$$(a-b)^2=a^2+b^2-2ab$$

Solution:

​$$\frac{a+1}{a}=k$$

$$\frac{a}{a}+\frac{1}{a} =k$$

$$1+\frac{1}{a}=k$$

$$\frac{1}{a}=k-1$$

$$a= \frac{1}{k-1}$$

$$a^2=\frac{1}{(k-1)^2}$$

​​​​​​​We need to find 

​$$\frac{a^2-1}{a^2}$$

$$=\frac{a^2}{a^2}-\frac{1}{a^2}$$

$$=1-\frac{1}{a^2}$$

substitute value $$a^2$$

$$1-\frac{1}{\frac{1}{\left(k-1\right)^2}}$$

$$=1-(k-1)^2$$

$$=1-(k^2+1-2k)$$

$$=1-k^2-1+2k$$

$$=2k-k^2$$

Thus, correct option is (a)