# How to resolve this fraction with change of divisors If i have an equation like this: a/(b cdot(c)/(d - f/g)) With what should I multiply to get g? Should I multiply it with d−f/g ? Or is this incorrect?

How to resolve this fraction with change of divisors
If i have an equation like this:
$\frac{a}{b\cdot \frac{c}{d-\frac{f}{g}}}$
With what should I multiply to get g?
Should I multiply it with $d-\frac{f}{g}$ ? Or is this incorrect?
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I would write
$\frac{16}{3-\frac{4}{x}}$
as
$\frac{16x}{3x-4}$
(multiplying by
$\frac{x}{x}$
) and further
$21-\frac{16x}{3x-4}=\frac{21\left(3x-4\right)-16x}{3x-4}$
and so on! the last term is (simplified)
$\frac{47x-84}{3x-4}$
and then we have
$3-\frac{7}{\frac{47x-84}{3x-4}}=\frac{3\left(47x-84\right)-7\left(3x-4\right)}{47x-84}=...$