Subtract the following rational expressions Reduce your answ

Subtract the following rational expressions. Reduce your answer to lowest terms. 2/t^2 - 4t - 5 - 1/t^2 - t - 2

Solution

{ 2 / ( t^2 - 4t - 5 ) } - { 1 / ( t^2 - t - 2 ) }

= 2 / (t-5)(t+1) - 1 / ( t- 2)(t+1)

lcd is (t-5) ( t-2) (t+1)

2 (t-2) / (t-5) ( t-2) (t+1) - 1 ( t-5) / (t-5) ( t-2) (t+1)

( 2t - 4 ) / (t-5) ( t-2) (t+1) - (1t - 5) /(t-5) ( t-2) (t+1)

( 2t - 4 -1t + 5 ) /(t-5) ( t-2) (t+1)

= ( t +1 ) / (t-5) ( t-2) (t+1)