Answer:
The sum of all the possible values for z that satisfy the above equation is -5.
Step-by-step explanation:
The given equation is
[tex]\frac{5}{z}-\frac{2z+4}{z+2}=-3[/tex]
We need to find the sum of all the possible values for z that satisfy the above equation.
The given equation can be rewritten as
[tex]\frac{5}{z}-\frac{2(z+2)}{z+2}=-3[/tex]
Cancel out common factors.
[tex]\frac{5}{z}-2=-3[/tex]
Add 2 on both sides.
[tex]\frac{5}{z}-2+2=-3+2[/tex]
[tex]\frac{5}{z}=-1[/tex]
[tex]5=-z[/tex]
Multiply both sides by -1.
[tex]-5=z[/tex]
Only z=-5 satisfy the given equation.
Therefore the sum of all the possible values for z that satisfy the above equation is -5.
