The problem is to solve the equation $M = \frac{n(v+w)}{v-w}$ for $v$. $M$, $n$, and $w$ are real numbers.

1. Problem Description

The problem is to solve the equation $M = \frac{n(v+w)}{v-w}$ for $v$. $M$, $n$, and $w$ are real numbers.

2. Solution Steps

We want to isolate $v$ in the equation $M = \frac{n(v+w)}{v-w}$.

First, multiply both sides of the equation by $(v-w)$:

$M(v-w) = n(v+w)$

$Mv - Mw = nv + nw$

Now, we want to collect the terms with $v$ on one side and the other terms on the other side. Subtract $nv$ from both sides:

$Mv - nv - Mw = nw$

Add $Mw$ to both sides:

$Mv - nv = nw + Mw$

Factor out $v$ from the left side:

$v(M-n) = nw + Mw$

Now, divide both sides by $(M-n)$, assuming $M \neq n$:

$v = \frac{nw + Mw}{M-n}$

We can also write this as:

$v = \frac{w(n+M)}{M-n}$

3. Final Answer

$v = \frac{w(M+n)}{M-n}$