Solve n+v/u-v=u

$$\frac { n + v } { u - v } = u$$

Solve for n

$$n=-\left(u\left(v-u\right)+v\right)$$

$$v\neq u$$

Solution Steps

Multiply both sides of the equation by u-v.

$$n+v=u\left(u-v\right)$$

Use the distributive property to multiply u by u-v.

$$n+v=u^{2}-uv$$

Subtract v from both sides.

$$n=u^{2}-uv-v$$

Solve for u

$$\left\{\begin{matrix}u=\frac{\sqrt{4n+v^{2}+4v}+v}{2}\text{, }&\left(v<0\text{ or }n\neq -v\right)\text{ and }n\geq -\frac{v^{2}}{4}-v\\u=\frac{-\sqrt{4n+v^{2}+4v}+v}{2}\text{, }&\left(v>0\text{ or }n\neq -v\right)\text{ and }n\geq -\frac{v^{2}}{4}-v\end{matrix}\right.$$