SOLUTION: Add. Simplify if possible. {{{(4t)/(t^2-1)+(t)/(t-1)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Add. Simplify if possible. {{{(4t)/(t^2-1)+(t)/(t-1)}}}      Log On


   

Question 396150: Add. Simplify if possible.
%284t%29%2F%28t%5E2-1%29%2B%28t%29%2F%28t-1%29
Found 3 solutions by MathLover1, nerdybill, CharlesG2:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%284t%29%2F%28t%5E2-1%29%2B%28t%29%2F%28t-1%29......you can factor %28t%5E2-1%29=+%28t%2B1%29%28t-1%29

%284t%29%2F%28t%5E2-1%29%2B%28t%29%2F%28t-1%29....common denominator is %28t%2B1%29%28t-1%29

%284t%2B%28t%29%28t%2B1%29%29%2F%28t%2B1%29%28t-1%29

%284t%2Bt%5E2%2Bt%29%2F%28t%2B1%29%28t-1%29

%28t%5E2+%2B+5t%29%2F%28t%2B1%29%28t-1%29

t%28t+%2B+5%29%2F%28t%2B1%29%28t-1%29



Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
%284t%29%2F%28t%5E2-1%29%2B%28t%29%2F%28t-1%29
Notice we can factor the denominator of the left term:
%284t%29%2F%28%28t%2B1%29%28t-1%29%29%2B%28t%29%2F%28t-1%29
%284t%29%2F%28%28t%2B1%29%28t-1%29%29%2Bt%28t%2B1%29%2F%28%28t%2B1%29%28t-1%29%29
%284t%29%2F%28%28t%2B1%29%28t-1%29%29%2B%28t%5E2%2Bt%29%2F%28%28t%2B1%29%28t-1%29%29
%284t%2Bt%5E2%2Bt%29%2F%28%28t%2B1%29%28t-1%29%29
%28t%5E2%2B5t%29%2F%28%28t%2B1%29%28t-1%29%29
t%28t%2B5%29%2F%28%28t%2B1%29%28t-1%29%29

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Add. Simplify if possible.
%284t%29%2F%28t%5E2-1%29%2B%28t%29%2F%28t-1%29

t^2 - 1 = (t + 1)(t - 1) by FOIL (First Outer Inner Last) middle terms cancel out in this case
%284t%29%2F%28t%5E2-1%29%2B%28t%29%28t%2B1%29%2F%28t-1%29%28t%2B1%29
needed common denominator so multiplied top and bottom on second fraction by t+1
%284t%2Bt%5E2%2Bt%29%2F%28t%5E2-1%29
%28t%5E2%2B5t%29%2F%28t%5E2-1%29