Question

Which expression will simplify to 1?

Answer 1

Let us check each Option :

$\mathsf{First\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}$

$\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}$

$\mathsf{Second\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{m + 9}\right)}$

$\mathsf{\implies 1}$

$\mathsf{Third\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 + m}{9 - m}\right)}$

$\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{-(m - 9)}\right)}$

$\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}$

$\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}$

$\mathsf{Fourth\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 - m}{9 + m}\right)}$

$\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{-(m - 9)}{9 + m}\right)}$

$\mathsf{\implies -\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{9 + m}\right)}$

$\mathsf{\implies -1\;\neq\;1}$

Answer : Option (2)