Question

Prove that, $(100-100)$ Divided by $(100-100)$ is equal to $2$.

Answer 1

Proof: Simplify the given expression.

We have to prove $\frac{100-100}{100-100}=2$.

Consider the LHS of the above expression.

$$\begin{gathered} \mathrm{LHS}=\frac{100-100}{100-100} \\ \Rightarrow =\frac{{10}^2-{10}^2}{10(10-10)} \\ \Rightarrow =\frac{(10-10)(10+10)}{10(10-10)}\left[\because a^2-b^2=(a-b)(a+b)\right] \\ \Rightarrow =\frac{10+10}{10} \\ \Rightarrow =\frac{20}{10} \\ \Rightarrow =2 \\ \Rightarrow =\mathrm{RHS} \end{gathered}$$

Hence proved.