Solve y/p+y/1-p=n/1-p

$$\frac { y } { p } + \frac { y } { 1 - p } = \frac { n } { 1 - p }$$

Solve for n

$$n=\frac{y}{p}$$

$$p\neq 0\text{ and }p\neq 1$$

Steps for Solving Linear Equation

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

$$\left(p-1\right)y-py=-pn$$

Use the distributive property to multiply p-1 by y.

$$py-y-py=-pn$$

Combine py and -py to get 0.

$$-y=-pn$$

Swap sides so that all variable terms are on the left hand side.

$$-pn=-y$$

Cancel out -1 on both sides.

$$pn=y$$

Divide both sides by p.

$$\frac{pn}{p}=\frac{y}{p}$$

Dividing by p undoes the multiplication by p.

$$n=\frac{y}{p}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{y}{n}\text{, }&y\neq 0\text{ and }y\neq n\text{ and }n\neq 0\\p\in \mathrm{R}\setminus 0,1\text{, }&y=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(p-1\right)y-py=-pn$$

Use the distributive property to multiply p-1 by y.

$$py-y-py=-pn$$

Combine py and -py to get 0.

$$-y=-pn$$

Swap sides so that all variable terms are on the left hand side.

$$-pn=-y$$

Cancel out -1 on both sides.

$$pn=y$$

The equation is in standard form.

$$np=y$$

Divide both sides by n.

$$\frac{np}{n}=\frac{y}{n}$$

Dividing by n undoes the multiplication by n.

$$p=\frac{y}{n}$$

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

$$p=\frac{y}{n}\text{, }p\neq 1\text{ and }p\neq 0$$