Solve r/d_{1}+r/d_{2}=5

$$\frac { r } { d _ { 1 } } + \frac { r } { d _ { 2 } } = 5$$

Solve for d_1

$$d_{1}=-\frac{d_{2}r}{r-5d_{2}}$$

$$d_{2}\neq 0\text{ and }r\neq 0\text{ and }r\neq 5d_{2}$$

Steps for Solving Linear Equation

Variable d_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d_{1}d_{2}, the least common multiple of d_{1},d_{2}.

$$d_{2}r+d_{1}r=5d_{1}d_{2}$$

Subtract 5d_{1}d_{2} from both sides.

$$d_{2}r+d_{1}r-5d_{1}d_{2}=0$$

Subtract d_{2}r from both sides. Anything subtracted from zero gives its negation.

$$d_{1}r-5d_{1}d_{2}=-d_{2}r$$

Combine all terms containing d_{1}.

$$\left(r-5d_{2}\right)d_{1}=-d_{2}r$$

Divide both sides by r-5d_{2}.

$$\frac{\left(r-5d_{2}\right)d_{1}}{r-5d_{2}}=-\frac{d_{2}r}{r-5d_{2}}$$

Dividing by r-5d_{2} undoes the multiplication by r-5d_{2}.

$$d_{1}=-\frac{d_{2}r}{r-5d_{2}}$$

Variable d_{1} cannot be equal to 0.

$$d_{1}=-\frac{d_{2}r}{r-5d_{2}}\text{, }d_{1}\neq 0$$

Solve for d_2

$$d_{2}=-\frac{d_{1}r}{r-5d_{1}}$$

$$d_{1}\neq 0\text{ and }r\neq 0\text{ and }r\neq 5d_{1}$$

Steps for Solving Linear Equation

Variable d_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d_{1}d_{2}, the least common multiple of d_{1},d_{2}.

$$d_{2}r+d_{1}r=5d_{1}d_{2}$$

Subtract 5d_{1}d_{2} from both sides.

$$d_{2}r+d_{1}r-5d_{1}d_{2}=0$$

Subtract d_{1}r from both sides. Anything subtracted from zero gives its negation.

$$d_{2}r-5d_{1}d_{2}=-d_{1}r$$

Combine all terms containing d_{2}.

$$\left(r-5d_{1}\right)d_{2}=-d_{1}r$$

Divide both sides by r-5d_{1}.

$$\frac{\left(r-5d_{1}\right)d_{2}}{r-5d_{1}}=-\frac{d_{1}r}{r-5d_{1}}$$

Dividing by r-5d_{1} undoes the multiplication by r-5d_{1}.

$$d_{2}=-\frac{d_{1}r}{r-5d_{1}}$$

Variable d_{2} cannot be equal to 0.

$$d_{2}=-\frac{d_{1}r}{r-5d_{1}}\text{, }d_{2}\neq 0$$