Question

What is the value of $$\left[ 2-3\left( 2-3\right)^{-1} \right]^{-1} $$?
A) 5
B) -5
C) $$\dfrac{1}{5}$$
D) $$\dfrac{-1}{5}$$

Answer 1

Hint: In this question it is given that we have to find the value of $$\left[ 2-3\left( 2-3\right)^{-1} \right]^{-1} $$. So to simplify this we have to follow the BODMAS rule, BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction, i.e, we have to first simply those operations which is under brackets and then division, after that multiplication then addition and subtraction.
Complete step-by-step solution:
So we are going to simplify $$\left[ 2-3\left( 2-3\right)^{-1} \right]^{-1} $$
So, $$\left[ 2-3\left( 2-3\right)^{-1} \right]^{-1} $$
=$$\left[ 2-3\left( -1\right)^{-1} \right]^{-1} $$
As we know that $$a^{-1}=\dfrac{1}{a}$$, so by using this,
=$$\left[ 2-3\times \dfrac{1}{-1} \right]^{-1} $$ [ $$\because \dfrac{1}{-1} =-1$$]
=$$\left[ 2-3\times \left( -1\right) \right]^{-1} $$
=$$\left[ 2-\left( -3\right) \right]^{-1} $$
=$$\left[ 2+3\right]^{-1} $$
=$$5^{-1}$$
=$$\dfrac{1}{5}$$
Therefore the required solution is $$\dfrac{1}{5}$$.
Hence the correct option is option C.
Note: To solve this type of question you have to keep in mind that always observe which part of this simplification needs to be simplified first. Like we have already introduced the BODMAS rule, so, by this rule you have to proceed. We can do subtraction before addition as well that will not affect the result.