T^3-t/t^3-t^2 simplify

Question

Simplify rational expression steps please I know the answer is t+1/t but how do u get thete

Answer 1

Assuming your question is simplify (t³-t)/(t³-t²), we can first factor t from the numerator and t² from the denominator.  We basically factor the lowest degree term from each expression (since the lowest deg term is common in every term of the expression).

 

We hence have t(t²-1)/(t²(t-1))=(t²-1)/(t(t-1)) obtained through dividing numerator and denominator by t (assuming t non-zero).

 

Then, we can once again factor...the denominator is already factored (being a product of linear terms); the numerator can be factored into (t-1)(t+1) via difference of squares.

 

Assuming t is not equal to 1 (else we would be dividing by 0), we can now divide both num and denom by t-1, obtaining (t+1)/t.

 

At this point we could distribute the 1/t to obtain 1+1/t, which concurs with your answer.

 

Hope this helps :)