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

Question 151771: z+3/z+1=z^2+9z+20/z^2-z-2 look for the root
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Note that

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

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.

RELATED QUESTIONS
z^2+9z+18 (answered by stanbon)

Solve for z:... (answered by Seutip)

simplify by removing factors of 1... (answered by Gogonati)

Z^3+27/Z^3-3Z^2+9Z (answered by jsmallt9)

1+Z+Z^2+Z^3...=1/Z-1 (answered by richard1234)

If -2 is a root of ((z^3) - (8(z^2)) + (9z) + 58 = 0, what are the other two... (answered by ikleyn)

simplify by removing factors of 1.... (answered by jim_thompson5910)

Good morning! An interesting radical conundrum for me: SIMPLIFY: fourth root of (9 (answered by Fombitz,CharlesG2,solver91311)

Solve the polynomial inequality... (answered by scott8148)