Question 1186361
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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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<pre>
My interior voice tells me that the equation is


    {{{6/(z-6)}}} - {{{2/(z+6)}}} = {{{5/(z^2-36)}}}.


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


Transform equivalently


    {{{(6*(z+6) - 2*(z-6))/((z+6)*(z-6))}}} = {{{5/(z^2-6)}}}

    {{{(4z + 48)/((z+6)*(z-6))}}} = {{{5/((z+6)*(z-6))}}}


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 = {{{-43/4}}} = -10 {{{3/4}}} = -10.75.    <U>ANSWER</U>
</pre>

Solved.


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