1. ## help

i need help on solving problems like this one
(z+4/z+5)=(z+4/z+1)+1
solve for z

2. Originally Posted by DaProphet
i need help on solving problems like this one
(z+4/z+5)=(z+4/z+1)+1
solve for z
Do you mean this?

$
\frac{z+4}{z+5}\;=\;\frac{z+4}{z+1}+1
$

That is NOT what you have written.

Can you do anything with this part?

$
\frac{z+4}{z+1}+1
$

Perhaps $\frac{z+4}{z+1}+\frac{z+1}{z+1}$?

How did I get that? Does that make any difference?

3. the way that you wrote it out is the way that i was trying to write it out like
and im not cure about the second part

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 . . . .

5. this is a much better plot, the intersections are the values of z that solves the equation