Solve 5/V=y-1/x

$$\frac { 5 } { V } = y - \frac { 1 } { x }$$

Solve for x

$$x=-\frac{V}{5-Vy}$$

$$V\neq 0\text{ and }\left(y=0\text{ or }V\neq \frac{5}{y}\right)$$

Steps for Solving Linear Equation

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

$$x\times 5=Vxy-V$$

Subtract Vxy from both sides.

$$x\times 5-Vxy=-V$$

Reorder the terms.

$$-Vxy+5x=-V$$

Combine all terms containing x.

$$\left(-Vy+5\right)x=-V$$

The equation is in standard form.

$$\left(5-Vy\right)x=-V$$

Divide both sides by 5-Vy.

$$\frac{\left(5-Vy\right)x}{5-Vy}=-\frac{V}{5-Vy}$$

Dividing by 5-Vy undoes the multiplication by 5-Vy.

$$x=-\frac{V}{5-Vy}$$

Variable x cannot be equal to 0.

$$x=-\frac{V}{5-Vy}\text{, }x\neq 0$$

Solve for V

$$V=-\frac{5x}{1-xy}$$

$$x\neq 0\text{ and }y\neq \frac{1}{x}$$