SOLUTION: Solve the rational equation. If there is more than one correct answer, enter a comma separated list. 6/z−6−2/z+6=5/z^2−36

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Question 1186361: Solve the rational equation. If there is more than one correct answer, enter a comma separated list.
6/z−6−2/z+6=5/z^2−36

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


I know what the real equation is supposed to be....

However, I would also like to help you learn that parentheses are important in mathematics. So I will just point out that the equation as you show it,



is not a rational equation, and I will ask you to re-post the problem showing the equation correctly.
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
Solve the rational equation. If there is more than one correct answer, enter a comma separated list.
6/z−6−2/z+6=5/z^2−36
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

My interior voice tells me that the equation is


     -  = .


The domain (the set of alloved values for z) is the entire number line except of two hole points -6 and 6).


Transform equivalently


     = 

     = 


Since we work in the domain, we can cancel (z+6)*(z-6) in the denominators.  We get then


    4z + 48 = 5

    4z = 5 - 48

    4z = -43

     z =  = -10  = -10.75.    ANSWER

Solved.

I checked my answer numerically by substituting the found value of z into the original equation. It works correctly.



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