SOLUTION: What are the values of z satisfying the equation? -2z/z-8=4/z^2-5z-24

Question 60654: What are the values of z satisfying the equation?
-2z/z-8=4/z^2-5z-24
Answer by asha(30) (Show Source): You can put this solution on YOUR website!
the sum is -2z/z-8 =4/z^2-5z-24
-2z/z-8 =4/(z-8)(z+3) by splitting the middle term such that
sum is -5 and product is-24,we get factors
-8 and +3
=>-z =2/z+3 cancelling common term 2 and z-8
-z(z+3) =2
-z^2-3z-2=0
z^2 + 3z +2 =0
z^2 +z +2z +2=0 splitting the middle term such that sum is3 and product is2
z(z+1)+2(z+1)=0
(z+1)(z+2)=0
z=-1 or z=-2 is the answer.
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