i need help on solving problems like this one

(z+4/z+5)=(z+4/z+1)+1

solve for z

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- Sep 4th 2009, 04:46 PM #1

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- Sep 4th 2009, 06:17 PM #2

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- Sep 4th 2009, 09:42 PM #3

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- Sep 4th 2009, 09:47 PM #4
,

Solving for z, you may multiply both sides with (z + 5)(z + 1), we get

(z + 4)(z + 1) = (z + 4)(z + 5) + (z + 5)(z + 1),

z^2 + 5z + 4 = z^2 +9z + 20 + z^2 + 6z + 5, rearranging

0 = (z^2 + z^2 - z^2) + (9z + 6z - 5z) + (20 + 5 - 4)

0 = z^2 + 10z + 21, factoring

0 = (z + 7)(z + 3),

thus, z = -3 and -7

I have plotted it below, see . . . .

- Sep 4th 2009, 09:49 PM #5