Verified answer

Based on the answer, they probably meant 1/(t+6) - 1/t.

Then the common denominator we need is t*(t+6)

For the first fraction, bottom needs a t but then we have to multiply top and bottom by t so we change the look but not the meaning-> 1/(t+6) =(1*t)/( (t+6)*t ) = t/( t*(t+6) )

Same idea on the second fraction where the needed factor is (t+6) -> (1*(t+6) )/ (t*(t+6)) = (t+6)/ (t*(t+6)).

In the main problem 1/(t+6) - 1/t -> t/( t*(t+6) ) - (t+6)/( t*(t+6) )

Since these have the common denominator just bring it together as

(t - (t+6)) / ( t*(t+6) )= (t - t -6 ) / ( t*(t+6) ) = -6/( t*(t+6) )

1/t + 6 - 1/t = 6

6 is the answer.

see step by step solution:

http://symbolab.com/solutions/join_fractions?query...