SOLUTION: Perform the indicated operation and simplify the result. Leave your answer in factored form. (x+4)/(x-5) - ((x-6)/(x+1))/(x+1)

Algebra ->  Rational-functions -> SOLUTION: Perform the indicated operation and simplify the result. Leave your answer in factored form. (x+4)/(x-5) - ((x-6)/(x+1))/(x+1)      Log On


   

Question 1048600: Perform the indicated operation and simplify the result. Leave your answer in factored form.

(x+4)/(x-5) - ((x-6)/(x+1))/(x+1)
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!


%28x%2B4%29%2F%28x-5%29-%28%28x-6%29%2F%28x%2B1%29%29%2F%28x%2B1%29

%28x%2B4%29%2F%28x-5%29-%28%28x-6%29%2F%28x%2B1%29%29%2A%281%2F%28x%2B1%29%29

%28x%5E%22%22%2B4%29%2F%28x%5E%22%22-5%29-%28x%5E%22%22-6%29%2F%28x%2B1%29%5E2%29

LCD = (x-5)(x+1)2

%28%28x%2B4%29%28x%2B1%29%5E2-%28x-6%29%28x-5%29%29%2F%28%28x-5%29%28x%2B1%29%5E2%29

%28%28x%2B4%29%28x%5E2%2B2x%2B1%29-%28x%5E2-11x%2B30%29%29%2F%28%28x-5%29%28x%2B1%29%5E2%29



%28x%5E3%2B2x%5E2%2Bx%2B4x%5E2%2B8x%2B4-x%5E2%2B11x-30%29%2F%28%28x-5%29%28x%2B1%29%5E2%29

%28x%5E3%2B5x%5E2%2B20x-26%29%2F%28%28x-5%29%28x%2B1%29%5E2%29

Now we analyze the polynomial x%5E3%2B5x%5E2%2B20x-26

candidates for zeros are ±1, ±2, ±13, ±26

We begin by trying +1 using synthetic division with
the factor theorem:

1|1  5  20 -26
 |   1   6  26
  1  6  26   0

That was fortunate.  The very first candidate for a
zero succeeded!

So x%5E3%2B5x%5E2%2B20x-26 factors as %28x-1%29%28x%5E2%2B6x%2B26%29
The quadratic does not factor, so the final result is:

%28%28x-1%29%28x%5E2%2B6x%2B26%29%29%2F%28%28x-5%29%28x%2B1%29%5E2%29

Edwin