Question

z 5 ​ − z+2 2z+4 ​ =−3 space, startfraction, 5, divided by, z, end fraction, minus, start fraction, 2, z, plus, 4, divided by, z, plus, 2, end fraction, equals, minus, 3 What is the sum of all the possible values for zzz that satisfy the equation above

Answer 1

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

$\frac{5}{z}-\frac{2z+4}{z+2}=-3$

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

$\frac{5}{z}-\frac{2(z+2)}{z+2}=-3$

Cancel out common factors.

$\frac{5}{z}-2=-3$

Add 2 on both sides.

$\frac{5}{z}-2+2=-3+2$

$\frac{5}{z}=-1$

$5=-z$

Multiply both sides by -1.

$-5=z$

Only z=-5 satisfy the given equation.

Therefore the sum of all the possible values for z that satisfy the above equation is -5.