Answer
$z=\frac{3}{97}$
Work Step by Step
$\displaystyle \frac{1}{z}-\frac{1}{2z}-\frac{1}{5z}=\frac{10}{z+1}$
We multiply both sides by $10z(z+1)$:
$10(z+1)-5(z+1)-2(z+1)=10(10z)$
Then we distribute and simplify:
$3(z+1)=100z$
$3z+3=100z$
$3=97z$
And solve for $z$:
$z=\frac{3}{97}$
