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

Algebra ->  Functions -> 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       Log On


   

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) About Me  (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,

6%2Fz-6-2%2Fz%2B6=5%2Fz%5E2-36

is not a rational equation, and I will ask you to re-post the problem showing the equation correctly.

Answer by ikleyn(52794) About Me  (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


    6%2F%28z-6%29 - 2%2F%28z%2B6%29 = 5%2F%28z%5E2-36%29.


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


Transform equivalently


    %286%2A%28z%2B6%29+-+2%2A%28z-6%29%29%2F%28%28z%2B6%29%2A%28z-6%29%29 = 5%2F%28z%5E2-6%29

    %284z+%2B+48%29%2F%28%28z%2B6%29%2A%28z-6%29%29 = 5%2F%28%28z%2B6%29%2A%28z-6%29%29


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 = -43%2F4 = -10 3%2F4 = -10.75.    ANSWER

Solved.

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