The problem asks us to rearrange the formula $h = \frac{mt}{d(m+p)}$ to make $m$ the subject.

1. Problem Description

The problem asks us to rearrange the formula $h = \frac{mt}{d(m+p)}$ to make $m$ the subject.

2. Solution Steps

We are given the equation:

$h = \frac{mt}{d(m+p)}$

First, multiply both sides by $d(m+p)$:

$hd(m+p) = mt$

Expand the left side:

$hdm + hdp = mt$

Rearrange the equation to isolate terms with $m$ on one side:

$hdp = mt - hdm$

Factor out $m$ from the right side:

$hdp = m(t - hd)$

Divide both sides by $(t - hd)$ to solve for $m$:

$m = \frac{hdp}{t - hd}$

3. Final Answer

$m = \frac{hdp}{t - hd}$