-8/(3z-1) + 9/(3z+1) = 5/(9z^2-1)

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

Multiply both sides by (3z-1)(3z+1):

-8(3z+1) +9(3z-1) = 5

-24z - 8 + 27z - 9 = 5

3z = 22

z = 22/3

-8/3z-1+9/3z+1=5/9z^2-1

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-8/(3z-1) + 9/(3z+1) = 5/(9z^2-1)

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

-8/(3z-1) + 9/(3z+1) = 5/((3z-1)(3z+1))

Multiply both sides by (3z-1)(3z+1):

-8(3z+1) +9(3z-1) = 5

-24z - 8 + 27z - 9 = 5

3z = 22

z = 22/3

(-8/3)z-1+(9/3)z+1=(5/9)z^2-1

simplify the left side

(1/3)z=(5/9)z^2-1

0=(5/9)z^2-(1/3)z-1

multiply both sides by 9

0=5z^2-3z-9

use the quadratic equation

[3+√9+180]/10

[3+√189]/10, but 189=9(21)

[3+3√21]/10

(3+3√21)/10 and (3-3√21)/10

-(5/9)z^2+(1/3)z+1=0

This equation can be solved using the quadratic equation.

x=(b±√(b

a=-5/9

b=1/3

c=1

Plug in the variables to the quadratic equation and solve.

Solve for "x", which is z in this problem. You will get two answers.

z=-1.07477 = -3(√21-1)/10

z=1.67477 = -3(√21+1)/10

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