Add or subtract. Then simplify. If a denominator has three or more facotrs (Other then monomials.) Leave it in factored form.

Question

Add or subtract. Then simplify. If a denominator has three or more facotrs (Other then monomials.) Leave it in factored form.

 

3x-1/x^2+2x-3  -  x+4/x^2-9

Answer 1

   (3x-1)            (x+4)

--------------  -  ---------

(x²+2x-3)        (x²-9)

 

Both denominators factor:

 

   (3x-1)            (x+4)
-------------- - -------------
(x+3)(x-1)     (x+3)(x-3)

 

Now put both rational expressions over a common denominator, (x+3)(x-3)(x-1):

 

(3x-1)(x-3) - (x+4)(x-1)

-------------------------------

     (x+3)(x-3)(x-1)

 

Multiply out the numerator and combine like terms:

 

3x²-9x-x+3-x²+x-4x+4

-------------------------------

     (x+3)(x-3)(x-1)

 

     2x²-13x-7

--------------------

(x+3)(x-3)(x-1)

 

The numerator factors:

 

  (2x+1)(x-7)

-------------------

(x+3)(x-3)(x-1)