If $\frac{a}{b}=\frac{1}{2}$ and $\frac{b}{c}=\frac{3}{4}$, then find the value of $\frac{a^2-c^2}{ac-bc}$.

$\frac{55}{24}$

$\frac{a}{b}=\frac{1}{2}$ and $\frac{b}{c}=\frac{3}{4}$

a : b = 1 : 2

b : c = 3 : 4

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a : b : c = 3 : 6 : 8

Now put all the values in the required equation,

$\frac{a^2-c^2}{ac-bc}$

= $\frac{3^2-8^2}{24-48}$ = $\frac{55}{24}$