Question 143996
{{{(1)/(z+1)-(6-z)/(6z)=0}}} Start with the given equation



{{{6z(z+1)((1)/(cross((z+1)))-(6-z)/(cross((6z))))=6z(z+1)(0)}}} Multiply both sides by the LCD {{{6z(z+1)}}}. Doing this will clear the fractions.




{{{6z-(z+1)(6-z)=0}}} Distribute and multiply



{{{6z-(-z^2+5z+6)=0}}} Foil



{{{6z+z^2-5z-6=0}}} Distribute



{{{z^2+z-6=0}}} Combine like terms




{{{(z+3)(z-2)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{z+3=0}}} or  {{{z-2=0}}} 


{{{z=-3}}} or  {{{z=2}}}    Now solve for z in each case



So our answers are


 {{{z=-3}}} or  {{{z=2}}}