How to resolve this fraction with change of divisors

Question

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?

Answer 1

i would write $$\frac{16}{3-\frac{4}{x}}$$ as $$\frac{16x}{3x-4}$$ (multiplying by $$\frac{x}{x}$$) and further $$21-\frac{16x}{3x-4}=\frac{21(3x-4)-16x}{3x-4}$$ and so on! the last term is (simplified) $$\frac{47x-84}{3x-4}$$ and then we have $$3-\frac{7}{\frac{47x-84}{3x-4}}=\frac{3(47x-84)-7(3x-4)}{47x-84}=...$$