u/p + u/q =m, if , p≠−q

q+u should be q+p

You want to solve for U maybe?

multiply both sides by pq
u q + u p = m p q
u (q+u) = m p q
u = m p q / (q+u)

that would be undefined (bottom = 0) if p = -q

oops, sorry

To solve the equation u/p + u/q = m, where p is not equal to -q, we need to isolate either u/p or u/q.

Let's try isolating u/p:
1. Start by subtracting u/q from both sides of the equation: u/p = m - u/q
2. Now, multiply both sides of the equation by p: u = p(m - u/q)
3. Distribute p to the terms within the parentheses: u = mp - u(p/q)
4. Add u(p/q) to both sides of the equation: u + u(p/q) = mp
5. Factor out u from the left side of the equation: u(1 + p/q) = mp
6. Finally, divide both sides of the equation by (1 + p/q): u = mp / (1 + p/q)

Now we have the value of u in terms of p, q, and m.