Answer
$3$
Work Step by Step
When we multiply the numerator and denominator of a rational expression with a nonzero expression,
we are multiplying the rational expression with 1.
Multiplying with 1 does not change the value, so the resulting rational expression is equivalent to the initial one..
Here, we have: initial rational expression = $\displaystyle \frac{7}{8x}$.
Multiply it with $1=\displaystyle \frac{A}{A}$, where A is some nonzero expression:
$\displaystyle \frac{7}{8x}\cdot 1=\frac{7}{8x}\cdot\frac{A}{A}=\frac{7A}{8x\cdot A}$,
We want the resulting denominator to be $24x$.
So, A must equal $3$, in which case
$\displaystyle \frac{7}{8x}=\frac{7}{8x}\cdot\frac{3}{3}=\frac{21}{24x}$
