Answer:
[tex]\displaystyle s = \frac{hz}{h-z}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle z = \frac{sh}{s+h}[/tex]
And we want to solve it for s.
First, we can multiply both sides by the denominator:
[tex]\displaystyle z(s+h) = sh[/tex]
Distribute:
[tex]\displaystyle sz + hz = sh[/tex]
Subtract hz and sh from both sides:
[tex]\displaystyle sz - sh = -hz[/tex]
Factor:
[tex]\displaystyle s(z-h) = -hz[/tex]
And divide. Hence:
[tex]\displaystyle s = \frac{-hz}{z-h} = - \frac{hz}{z-h} = \frac{hz}{h-z}[/tex]
Any one of the above three forms are correct, although the third form is preferred because it omits the additional negative.
