Solve um=m+3/m+1

$$u m = \frac { m + 3 } { m + 1 }$$

Solve for u

$$u=\frac{m+3}{m\left(m+1\right)}$$

$$m\neq -1\text{ and }m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m+1.

$$um\left(m+1\right)=m+3$$

Use the distributive property to multiply um by m+1.

$$um^{2}+um=m+3$$

Combine all terms containing u.

$$\left(m^{2}+m\right)u=m+3$$

Divide both sides by m^{2}+m.

$$\frac{\left(m^{2}+m\right)u}{m^{2}+m}=\frac{m+3}{m^{2}+m}$$

Dividing by m^{2}+m undoes the multiplication by m^{2}+m.

$$u=\frac{m+3}{m^{2}+m}$$

Divide m+3 by m^{2}+m.

$$u=\frac{m+3}{m\left(m+1\right)}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sqrt{u^{2}+10u+1}-u+1}{2u}\text{; }m=\frac{-\sqrt{u^{2}+10u+1}-u+1}{2u}\text{, }&u\leq -2\sqrt{6}-5\text{ or }\left(u\neq 0\text{ and }u\geq 2\sqrt{6}-5\right)\\m=-3\text{, }&u=0\end{matrix}\right.$$