Solve a-R/a=R/b

$$\frac { a - R } { a } = \frac { R } { b }$$

Solve for R

$$R=\frac{ab}{a+b}$$

$$a\neq -b\text{ and }a\neq 0\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\left(a-R\right)=aR$$

Use the distributive property to multiply b by a-R.

$$ba-bR=aR$$

Subtract aR from both sides.

$$ba-bR-aR=0$$

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

$$-bR-aR=-ba$$

Reorder the terms.

$$-Ra-Rb=-ab$$

Combine all terms containing R.

$$\left(-a-b\right)R=-ab$$

Divide both sides by -a-b.

$$\frac{\left(-a-b\right)R}{-a-b}=-\frac{ab}{-a-b}$$

Dividing by -a-b undoes the multiplication by -a-b.

$$R=-\frac{ab}{-a-b}$$

Divide -ab by -a-b.

$$R=\frac{ab}{a+b}$$

Solve for a

$$a=\frac{Rb}{b-R}$$

$$R\neq 0\text{ and }b\neq 0\text{ and }R\neq b$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ab, the least common multiple of a,b.

$$b\left(a-R\right)=aR$$

Use the distributive property to multiply b by a-R.

$$ba-bR=aR$$

Subtract aR from both sides.

$$ba-bR-aR=0$$

Add bR to both sides. Anything plus zero gives itself.

$$ba-aR=bR$$

Combine all terms containing a.

$$\left(b-R\right)a=bR$$

The equation is in standard form.

$$\left(b-R\right)a=Rb$$

Divide both sides by b-R.

$$\frac{\left(b-R\right)a}{b-R}=\frac{Rb}{b-R}$$

Dividing by b-R undoes the multiplication by b-R.

$$a=\frac{Rb}{b-R}$$

Variable a cannot be equal to 0.

$$a=\frac{Rb}{b-R}\text{, }a\neq 0$$