Express in Simplest form

Question

     36−x^2

     ----------

     (x+6)^2

 ----------------

        x-3

     ----------

   x^2+3x-18

 

 

Answer 1

To start this problem by factoring each polynomial like it did in the second part below. Next, because you are dividing fractions, the rule is the keep the first fraction, and take the reciprocal of the second fraction. In other words, flip the fraction. That's what is one in the 3rd section. Next you can eliminate any binomial groups  that are on opposite sides of the fractions. So notice the (x+6) and (6 +x) cancels, (x - 3) and (x - 3) cancels,  (x + 6) and (x + 6) cancels, which results to simplifying to (6 - x).

 

 

 

(6 - x)(6 + x)     ÷        x - 3             

(x + 6)(x + 6)          x² + 3x - 18                     

 

 

=   (6 - x)(6 + x)    ÷        x - 3

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

     (x + 6)(x + 6)         (x + 6)(x - 3)

 

 

 

 

= (6 - x)(6 + x) • (x + 6)(x - 3)

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

   (x + 6)(x + 6)         x - 3

 

          

=    (6 - x)     •      (x + 6)(x - 3)

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

       (x + 6)                 x - 3

 

=     (6 - x)     •        (x + 6)

      ----------           ------------
       (x + 6)                                                                                                                                                          

 

=      (6 - x)