Solve (5/3)^1-x^-1=d^-1

$$( \frac { 5 } { 3 } ) ^ { 1 } - x ^ { - 1 } = d ^ { - 1 }$$

Solve for d

$$d=\frac{3x}{5x-3}$$

$$x\neq 0\text{ and }x\neq \frac{3}{5}$$

Steps for Solving Linear Equation

Calculate \frac{5}{3} to the power of 1 and get \frac{5}{3}.

$$\frac{5}{3}-x^{-1}=d^{-1}$$

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

$$d^{-1}=\frac{5}{3}-x^{-1}$$

Reorder the terms.

$$\frac{1}{d}=\frac{5}{3}-\frac{1}{x}$$

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3dx, the least common multiple of d,3,x.

$$3x=3dx\times \frac{5}{3}-3d$$

Multiply 3 and \frac{5}{3} to get 5.

$$3x=5dx-3d$$

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

$$5dx-3d=3x$$

Combine all terms containing d.

$$\left(5x-3\right)d=3x$$

Divide both sides by 5x-3.

$$\frac{\left(5x-3\right)d}{5x-3}=\frac{3x}{5x-3}$$

Dividing by 5x-3 undoes the multiplication by 5x-3.

$$d=\frac{3x}{5x-3}$$

Variable d cannot be equal to 0.

$$d=\frac{3x}{5x-3}\text{, }d\neq 0$$

Solve for x

$$x=\frac{3d}{5d-3}$$

$$d\neq 0\text{ and }d\neq \frac{3}{5}$$

Steps for Solving Linear Equation

Calculate \frac{5}{3} to the power of 1 and get \frac{5}{3}.

$$\frac{5}{3}-x^{-1}=d^{-1}$$

Reorder the terms.

$$\frac{5}{3}-\frac{1}{x}=\frac{1}{d}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3dx, the least common multiple of 3,x,d.

$$3dx\times \frac{5}{3}-3d=3x$$

Multiply 3 and \frac{5}{3} to get 5.

$$5dx-3d=3x$$

Subtract 3x from both sides.

$$5dx-3d-3x=0$$

Add 3d to both sides. Anything plus zero gives itself.

$$5dx-3x=3d$$

Combine all terms containing x.

$$\left(5d-3\right)x=3d$$

Divide both sides by -3+5d.

$$\frac{\left(5d-3\right)x}{5d-3}=\frac{3d}{5d-3}$$

Dividing by -3+5d undoes the multiplication by -3+5d.

$$x=\frac{3d}{5d-3}$$

Variable x cannot be equal to 0.

$$x=\frac{3d}{5d-3}\text{, }x\neq 0$$