(x-y)/x=z Solve For X

Jasonbradley

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Jun 17, 2024

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Solving for x in the Equation (x-y)/x = z

This article will guide you through the steps of solving for x in the equation (x-y)/x = z.

Understanding the Equation

The equation (x-y)/x = z represents a relationship between three variables:

• x: The unknown variable we want to solve for.
• y: A known constant.
• z: A known constant.

Solving for x

Let's break down the process of solving for x:

1. Multiply both sides by x: This eliminates the fraction on the left side. (x-y)/x * x = z * x This simplifies to: x - y = zx

2. Subtract zx from both sides: This isolates the x terms on one side of the equation. x - y - zx = zx - zx This simplifies to: x - y - zx = 0

3. Factor out x: This allows us to combine the x terms. x(1 - z) - y = 0

4. Add y to both sides: This moves the y term to the right side. x(1 - z) = y

5. Divide both sides by (1 - z): This isolates x on the left side. x = y / (1 - z)

Final Solution

Therefore, the solution for x in the equation (x-y)/x = z is x = y / (1 - z).

Important Note:

It's important to note that the solution is only valid if (1 - z) ≠ 0. If (1 - z) = 0, then the equation becomes undefined, and there is no solution for x.