Question

simplify and express with a common denominator 1/m+2/m+1 +3/m-2

Answer 1

Hey there !

Solution:

$\text{ Given} = \dfrac{1}{m} + \dfrac{2}{m + 1 } + \dfrac{3}{m - 2 } \\ \\ \text{ Taking LCM we get,} \\ \\ \implies LCM = ( m )(m + 1 )(m - 2 ) \\ \\ \implies \dfrac{ 1 ( m+1)(m-2) + 2 ( m)(m-2) + 3 ( m ) ( m + 1 )}{(m)(m+1)(m-2)} \\ \\ \implies \dfrac{ m^2 -2m + m - 2 + 2 ( m^2 - 2m ) + 3 ( m^2 + m )}{ (m^2 + m)(m-2)} \\ \\ \implies \dfrac{ m^2 - m - 2 + 2m^2 - 4m + 3m^2 + 3m}{m^3 -2m^2 +m^2 - 2m} \\ \\ \implies \dfrac{6m^2 -2m -2 }{m^3 - m^2 -2m }$

This is the required answer !

Hope my answer helped !