Solve 1/{P_{1}{x}_{1}-5{P}_{1}}=1/{P_{2}{x}_{2}}

$$\frac{ 1 }{ { P }_{ 1 } { x }_{ 1 } -5 { P }_{ 1 } } = \frac{ 1 }{ { P }_{ 2 } { x }_{ 2 } }$$

Solve for P_1

$$P_{1}=\frac{P_{2}x_{2}}{x_{1}-5}$$

$$x_{2}\neq 0\text{ and }P_{2}\neq 0\text{ and }x_{1}\neq 5$$

Steps for Solving Linear Equation

Variable P_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{1}P_{2}x_{2}\left(x_{1}-5\right), the least common multiple of P_{1}x_{1}-5P_{1},P_{2}x_{2}.

$$P_{2}x_{2}=P_{1}\left(x_{1}-5\right)$$

Use the distributive property to multiply P_{1} by x_{1}-5.

$$P_{2}x_{2}=P_{1}x_{1}-5P_{1}$$

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

$$P_{1}x_{1}-5P_{1}=P_{2}x_{2}$$

Combine all terms containing P_{1}.

$$\left(x_{1}-5\right)P_{1}=P_{2}x_{2}$$

Divide both sides by x_{1}-5.

$$\frac{\left(x_{1}-5\right)P_{1}}{x_{1}-5}=\frac{P_{2}x_{2}}{x_{1}-5}$$

Dividing by x_{1}-5 undoes the multiplication by x_{1}-5.

$$P_{1}=\frac{P_{2}x_{2}}{x_{1}-5}$$

Variable P_{1} cannot be equal to 0.

$$P_{1}=\frac{P_{2}x_{2}}{x_{1}-5}\text{, }P_{1}\neq 0$$

Solve for P_2

$$P_{2}=\frac{P_{1}\left(x_{1}-5\right)}{x_{2}}$$

$$x_{1}\neq 5\text{ and }P_{1}\neq 0\text{ and }x_{2}\neq 0$$

Steps for Solving Linear Equation

Variable P_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{1}P_{2}x_{2}\left(x_{1}-5\right), the least common multiple of P_{1}x_{1}-5P_{1},P_{2}x_{2}.

$$P_{2}x_{2}=P_{1}\left(x_{1}-5\right)$$

Use the distributive property to multiply P_{1} by x_{1}-5.

$$P_{2}x_{2}=P_{1}x_{1}-5P_{1}$$

The equation is in standard form.

$$x_{2}P_{2}=P_{1}x_{1}-5P_{1}$$

Divide both sides by x_{2}.

$$\frac{x_{2}P_{2}}{x_{2}}=\frac{P_{1}\left(x_{1}-5\right)}{x_{2}}$$

Dividing by x_{2} undoes the multiplication by x_{2}.

$$P_{2}=\frac{P_{1}\left(x_{1}-5\right)}{x_{2}}$$

Variable P_{2} cannot be equal to 0.

$$P_{2}=\frac{P_{1}\left(x_{1}-5\right)}{x_{2}}\text{, }P_{2}\neq 0$$