Solve m/n+1+m+1/n=m/n

$$\frac{ m }{ n+1 } + \frac{ m+1 }{ n } = \frac{ m }{ n }$$

Solve for m

$$m=-1-\frac{1}{n}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by n\left(n+1\right), the least common multiple of n+1,n.

$$nm+\left(n+1\right)\left(m+1\right)=\left(n+1\right)m$$

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

$$nm+nm+n+m+1=\left(n+1\right)m$$

Combine nm and nm to get 2nm.

$$2nm+n+m+1=\left(n+1\right)m$$

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

$$2nm+n+m+1=nm+m$$

Subtract nm from both sides.

$$2nm+n+m+1-nm=m$$

Combine 2nm and -nm to get nm.

$$nm+n+m+1=m$$

Subtract m from both sides.

$$nm+n+m+1-m=0$$

Combine m and -m to get 0.

$$nm+n+1=0$$

Subtract n from both sides. Anything subtracted from zero gives its negation.

$$nm+1=-n$$

Subtract 1 from both sides.

$$nm=-n-1$$

Divide both sides by n.

$$\frac{nm}{n}=\frac{-n-1}{n}$$

Dividing by n undoes the multiplication by n.

$$m=\frac{-n-1}{n}$$

Divide -n-1 by n.

$$m=-1-\frac{1}{n}$$

Solve for n

$$n=-\frac{1}{m+1}$$

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

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by n\left(n+1\right), the least common multiple of n+1,n.

$$nm+\left(n+1\right)\left(m+1\right)=\left(n+1\right)m$$

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

$$nm+nm+n+m+1=\left(n+1\right)m$$

Combine nm and nm to get 2nm.

$$2nm+n+m+1=\left(n+1\right)m$$

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

$$2nm+n+m+1=nm+m$$

Subtract nm from both sides.

$$2nm+n+m+1-nm=m$$

Combine 2nm and -nm to get nm.

$$nm+n+m+1=m$$

Subtract m from both sides.

$$nm+n+1=m-m$$

Combine m and -m to get 0.

$$nm+n+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$nm+n=-1$$

Combine all terms containing n.

$$\left(m+1\right)n=-1$$

Divide both sides by m+1.

$$\frac{\left(m+1\right)n}{m+1}=-\frac{1}{m+1}$$

Dividing by m+1 undoes the multiplication by m+1.

$$n=-\frac{1}{m+1}$$

Variable n cannot be equal to any of the values -1,0.

$$n=-\frac{1}{m+1}\text{, }n\neq -1\text{ and }n\neq 0$$