SOLUTION: z+3/z+1=z^2+9z+20/z^2-z-2 look for the root

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Question 151771: z+3/z+1=z^2+9z+20/z^2-z-2 look for the root
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Note that
z%5E2+%2B+9z+%2B+20+=+%28z+%2B+4%29%28z+%2B+5%29
z%5E2+-+z+-+2+=+%28z+-+2%29%28z+%2B+1%29
So the original equation becomes:

Multiplying both sides by (z - 2)(z + 1), we have
(z + 3)(z - 2) = (z + 4)(z + 5)
Expanding, we have
z%5E2+%2B+z+-+6+=+z%5E2+%2B+9z+%2B+20
Simplifying, we have
-26 = 8z
z = -26/8 = -13/4
CHECK:
Left hand side = (-13/4) + 3)/(-13/4 + 1) = 1/9
Right hand side = [(-13/4)^2 + 9(-13/4) + 20]/[(-13/4)^2 - (-13/4) - 2]= 1/9
So z = -13/4 is the root of the original equation.